Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1201154: Hello, please i need your assistant to solve this;
In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?
Sample size: freshmen 50, seniors 60
Sample mean freshmen $480, seniors $500
Population std.dev. freshmen $52, seniors $63
Click here to see answer by Theo(13342)   |
Question 1201531: Bad gums may mean a bad mood. Researchers discovered that 85% of people who
have suffered a bad mood had periodontal disease, an inflammation of the gums. Only 29%
of healthy people have this disease. Suppose that in a certain community bad moods are
quite rare, occurring with only 10% probability. If someone has periodontal disease, what
is the probability that he or she will have a bad mood?
Click here to see answer by Glaviolette(140)  |
Question 1201540: 1.The following salaries (in pesos) were obtained from a sample of 12 executive secretaries:
7,500 13,000 10,300 10,600 7,600 8,350
8,400 5,800 6,300 9,200 7,500 9,470
(a)Find estimates for the mean and variance of the salaries of all executive secretaries.
(b) What is the proportion of executive secretaries with salaries above P9,000.
Click here to see answer by Glaviolette(140) |
Question 1201540: 1.The following salaries (in pesos) were obtained from a sample of 12 executive secretaries:
7,500 13,000 10,300 10,600 7,600 8,350
8,400 5,800 6,300 9,200 7,500 9,470
(a)Find estimates for the mean and variance of the salaries of all executive secretaries.
(b) What is the proportion of executive secretaries with salaries above P9,000.
Click here to see answer by math_tutor2020(3816) |
Question 1201542: A distribution of values is normal with a mean of 99.5 and a standard deviation of 16.
Find P71, which is the score separating the bottom 71% from the top 29%.
P71 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The combined SAT scores for the students at a local high school are normally distributed with a mean of 1450 and a standard deviation of 307. The local college includes a minimum score of 2402 in its admission requirements.
What percentage of students from this school earn scores that fail to satisfy the admission requirement?
P(X < 2402) = %
Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1056 and a standard deviation of 205. Scores on the ACT test are normally distributed with a mean of 21.6 and a standard deviation of 4.6. It is assumed that the two tests measure the same aptitude, but use different scales.
If a student gets an SAT score that is the 54-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.
What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.
If a student gets an SAT score of 1569, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.
Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher’s hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean μ = 92.12 mph and a standard deviation of σ = 2.43 mph.
Compute the z-score of pitch with speed 87.4 mph. (Round your answer to two decimal places.)
Correct
Approximately what fraction of these four-seam fastballs would you expect to have speeds between 91.9 mph and 93.5 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)
Approximately what fraction of these four-seam fastballs would you expect to have speeds below 91.9 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)
A baseball fan wishes to identify the four-seam fastballs among the slowest 22% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 22%? (Round your answer to the nearest 0.1 mph.)
mph
Scores for a common standardized college aptitude test are normally distributed with a mean of 501 and a standard deviation of 105. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.
If 1 of the men is randomly selected, find the probability that his score is at least 566.6.
P(X > 566.6) =
Enter your answer as a number accurate to 4 decimal places.
If 16 of the men are randomly selected, find the probability that their mean score is at least 566.6.
P(M > 566.6) =
Enter your answer as a number accurate to 4 decimal places.
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 64 and 75?
ans = %
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 53 months and a standard deviation of 10 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 23 and 43 months?
ans =
Click here to see answer by ikleyn(52778)  |
Question 1200840: A manufacturer knows that their items have a normally distributed length, with a mean of 14.3 inches, and standard deviation of 1.7 inches.
If 12 items are chosen at random, what is the probability that their mean length is less than 14.2 inches?
Enter your answers as numbers accurate to 4 decimal places.
Click here to see answer by Theo(13342) |
Question 1201477: Suppose the quiz consists of 20 true - false questions.a student hasn't studied for the exam and will just be randomly guessing at all answers (with true and false equally likely). Explain how to find the probability that the student guess 8 or fewer answers correct.( just Explain the process)
Click here to see answer by greenestamps(13198)  |
Question 1201588: The data below represents the number of T-shirts sold per week by a student who started his own online t-shirt business. Find the weighted mean of the number of t-shirts sold per week. (Round your answer to the nearest tenth if necessary.)
T-Shirts Sold per Week Frequency
4 1
8 7
12 5
16 6
Click here to see answer by mananth(16946)  |
Question 1201593: 4. A box contains 500 envelopes of which 75 contain $100 in cash, 150 contain $25, and 275 contain $10. An envelope may be purchased for $25. What is the sample space for the different amounts of money? Assign probabilities to, the sample points and then find the probability that the first envelope purchased contains less than $100..
Click here to see answer by Glaviolette(140) |
Question 1201591: Trey has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.
This game is this: Trey chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an even numbered card is drawn. He loses $7 if an odd numbered card is drawn.
(a). Find the expected value of playing the game.
(b). What can Trey expect in the long run, after playing the game many times?
(He replaces the card in the deck each time.)
Click here to see answer by Glaviolette(140) |
Question 1201591: Trey has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.
This game is this: Trey chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an even numbered card is drawn. He loses $7 if an odd numbered card is drawn.
(a). Find the expected value of playing the game.
(b). What can Trey expect in the long run, after playing the game many times?
(He replaces the card in the deck each time.)
Click here to see answer by math_tutor2020(3816) |
Question 1201592: 4. A box contains 500 envelopes of which 75 contain $100 in cash, 150 contain $25, and 275 contain $10. An envelope may be purchased for $25. What is the sample space for the different amounts of money? Assign probabilities to, the sample points and then find the probability that the first envelope purchased contains less than $100..
Click here to see answer by Glaviolette(140) |
Question 1201602: APPLES: the annual per capita consumption of fresh apples
(in pounds) in the united states can be approximated by a normal distribution with a mean of 16.2 pounds and a standard deviation of 4 pounds
a. what is the smallest annual per capita consumption of apples can be in the top 25% pf consumption?
b. what is the largest annual per capita consumption of apples that can be in the bottom 15% of consumption?
Click here to see answer by ikleyn(52778) |
Question 1201610: Kevin has a bag with 8 balls numbered 1 through 8. He is playing a game of chance.
This game is this: Kevin chooses one ball from the bag at random. He wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. He loses $16 if 7 or 8 is selected.
(If necessary, consult a list of formulas.)
(a.) Find the expected value of playing the game.
(b.) What can Kevin expect in the long run, after playing the game many times?
(He replaces the ball in the bag each time.)
Click here to see answer by ikleyn(52778) |
Question 1201609: Assume that females have pulse rates that are normally distributed with a mean of = 76.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (C)
k below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 72 beats per minute and 80 beats per minute
The probability is
[Round to tour decimal o aces as needed.
b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean between 72 beats per minute and 80 beats per minute.
The probability is
(Round to four decimal places as needed.)
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
A. Since the original population has a normal distribution. the distribution of sample means is a normal distribution for any sample size
B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size
C. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size
D. Since the distribution is of sample means, not individuals. the distribution is a normal distribution for an sample size
Click here to see answer by math_tutor2020(3816) |
Question 1201601: 5. The distribution of survival time of guinea pigs with cancer after treatment is typically strongly right-skewed. Assume that the mean of the guinea pig survival time for a population of guinea pigs with cancer is 100 days with a standard deviation of 10 days. Suppose we take a sample of size n=49 guinea pigs from the population of guinea pigs with cancer.
(a) Explain why even though the population in this case is known to be skewed right we can model the sample mean using a Normal distribution.
(b) What is the approximate probability that the sample mean survival time will be less than 95 days?
(c) Determine the required sample size such that the probability that the sample mean will be within 2 days of the population mean survival time is 95%.
Click here to see answer by math_tutor2020(3816) |
Question 1201612: You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
A random sample of 55 home theater systems has a mean price of $117.00. Assume the population standard deviation is $18.30.
Click here to see answer by math_tutor2020(3816) |
Question 1201632: A distribution of values is normal with a mean of 58.2 and a standard deviation of 40.3.
Find P35, which is the score separating the bottom 35% from the top 65%.
P35 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Click here to see answer by Theo(13342) |
Question 1201631: A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1085 and a standard deviation of 199. Scores on the ACT test are normally distributed with a mean of 20.5 and a standard deviation of 3.8. It is assumed that the two tests measure the same aptitude, but use different scales.
If a student gets an SAT score that is the 61-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.
What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.
If a student gets an SAT score of 1543, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.
Click here to see answer by Theo(13342) |
Question 1201652: A box contains 1 plain pencil and 9 pens. A second box contains 3 colored pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a colored pencil from the second box is selected?
Write your answer as a fraction in simplest form.
How do I write this as a fraction in simplest form?
Click here to see answer by ikleyn(52778) |
Question 1201653: The life expectancy of light bulbs whose lifetimes are normally distributed with a mean life of 750 hours and with a standard deviation of 80 hours. Show or explain how you determine the appropriate z-score and related percentage.
What percent of light bulbs will last longer than 870 hours?
What percent of light bulbs will last between 730 hours and 850 hours?
What percent of light bulbs will last less than 770 hours?
Inverse Normal Distribution: If the quality control program of the company can consistently eliminate the worst 10% of the bulbs manufactured, the manufacturer can safely offer customers a money-back guarantee on all lights that fail before [_____] hours of burning time.
-----
Thank you!
Click here to see answer by math_tutor2020(3816) |
Question 1201654: A distribution of values is normal with a mean of 180.9 and a standard deviation of 83.6.
Find P42, which is the score separating the bottom 42% from the top 58%.
P42 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Click here to see answer by Theo(13342) |
Question 1201682: A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 124 people living in Gastown and finds that 20 have an annual income that is below the poverty line.
Part i) The proportion of the 124 people who are living below the poverty line, 20/124, is a:
A. parameter.
B. statistic.
C. variable of interest.
Part ii) Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line.
(Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
95% confidence interval = ( , )
Click here to see answer by math_tutor2020(3816) |
Question 1201687: probability of arriving in the hall when the laser is emitting blue. yellow and green light. Assuming that out of each minute blue is operating for 45 seconds, yellow for 10 and green for 5 seconds. State the probability of arriving in the hall when the laser is emitting the blue light?
Click here to see answer by ikleyn(52778) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 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