Questions on Algebra: Probability and statistics answered by real tutors!

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Question 356787: In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force. $157, $132, $109, $145, $125, $139
a) Calculate x/- (should be - over x), s/2 (s squared), and s for the expenses data. In addition, show that the two different formulas for calculating s/2 give the same result.
b) Assuming that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force.
c) If a member of the sales force submits an entertainment expense (dinner cost for four) of $190, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer.
d) Compute and interpret the z-score for each of the six entertainment expenses.

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Question 595250: Toss a penny, nickel, dime and quarter together. How many heads/tails arrangements are possible? Of those, how many have two heads and two tails?
My attempts:
(2C1)*(2C1)*(2C1)*(2C1)=16 possible combinations
How can I find out how many combinations have 2 head and 2 tails? Am I on the right track?

Click here to see answer by jim_thompson5910(28593) About Me 

Question 595370: Three cards are drawn, without replacement, from a standard deck of fifty-tow cards. Find the probability of these events.
a). Getting three kings
b). Getting a ten, nine, and eight in order
c). Getting a diamon, heart, and club in order.

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Question 595319: out of 9000 college students surveyed, 540 responded that they do not eat breakfast. what percent of students do not eat breakfast
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Question 595423: Bob is moving and all of his CDs are mixed up in a box. Twelve CDs are rock, eight are jazz, and five are classical. If he reaches in the box and selects them at random, find each possibility.
A). P ( 1 classical, 2 jazz)
B). P ( 1 jazz, 2 rock)
C). P ( 2 rock, 2 classical)

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Question 595393: Forty percent of banks did not earn profits during 2003. The SEC selects two banks at random. Find the probability that neither of them earned profits in 2003.
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Question 595519: Mr Scott is rolling a cube with faces numbered from 1 through 6. What is the likelihood that mr Scott will roll an 8
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Question 595533: The odds against a horse winning a race are 8:5. Find the probability that the horse will win the race?
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Question 595565: In how many ways can first, second, and third prizes be awarded in a contest with 650 contestants?
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Question 595567: Standard automobile license plates in a country display 1 numbers, followed by 3 letters, followed by 3 numbers. How many different standard plates are possible in this system? (Assume lead 0 is not allowed, but repetitions of letters and numbers are allowed.)
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Question 595628: A ball is thrown straight upward with an initial velocity of 52 ft/sec. Its height above the ground after seconds is given by the formula h(t)=-16t^2+52t. Whta is the maximum height that the ball attains before hitting the ground (feet)?
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Question 595632: Why do pirates search for treasure instead of anything else?
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Question 595596: There are 16 male names and 8 female names in a box. What is the probability of drawing a female name?
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Question 595804: Two cards are selected at random Of a deck of 20 cards ranging from 1 to 5 with monkeys, frogs, lions, and birds on them all numbered 1 through 5 . Determine the probability of the following
• a) with replacement.
• b) without replacement.
The first shows a 2, and the second shows a 4

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Question 595803: 100 calculators 2 are defected. I buy 8 what is the probability that I will get a defected one
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Question 595707: A committee of four members is to be randomly formed from eight technicians, four engineers, and three mathematicians. What is the probability that the committee will not be comprised of mathematicians only?
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Question 595829: When analyzing the last digits of telephone numbers in Port Jefferson, it is found taht among 1000 randomly selected digits, 119 are zeros. If the digits are randonly selected, the proportion of zeros should be 0.1.
Use the traditional method with .05 significance level to test the claim that the proportion of zeros equals 0.1
Use the P Value method with a .05 significance level to test the claim that the propartion of zeros equals 0.1

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Question 595828: A researcher believes that most swimming champions are men. He collects the names and sexes of the past 20 all-time swimming champions in the US. He finds that 16 of them are men. However, it is also well-known that 70% of professional swimmers are men.
a. What is the probability that out of 20 swimming champions, 16 of them are men?
b. What is the critical value to test our hypothesis using an alpha level of .05?
c. What is the critical value (in terms of # of men) if our alpha level was .01?
d. What is the p-value for the researcher’s observed outcome?
e. Make a decision about the researcher’s hypothesis, using an alpha level of .01.

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Question 595885: On a certain biased coin, heads is twice as likely as tails. That is, P(H) = 2/3.
What is the expected number of heads in 900 tosses?

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Question 595840: There are 8 red marbles and 8 blue marbles in a bag. Find the probability of choosing 2 red marbles without replacement.
A. 7/24
B. 30/60
C. 7/30
D. 15/32

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Question 596022: Using two independent samples, we test for a hypothesized difference between two population means. The population standard deviations are equal. The number in the first sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value?
a.24
b.25
c.26
d.27

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Question 596028: A recent national survey found that high school students watched an average (mean) of 7.3 DVDs per month with a population standard deviation of .50 hours. A random sample of 40 college students revealed that the mean number of DVDs watched last month was 6.60. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students and Compute the value of the test statistic ?
(I can't find the test statistic part)

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Question 596030: A recent national survey found that high school students watched an average (mean) of 7.3 DVDs per month with a population standard deviation of .50 hours. A random sample of 40 college students revealed that the mean number of DVDs watched last month was 6.60. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students and Compute the P-value ?
(I know I just asked a very similar question but now I can't find the p-value and i'm not sure what that is)

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Question 596060: Should companies use the same confidence interval each time a confidence interval is determined or should the level change based on situations? If it changes based on situations, what type of situations might call for higher confidence levels?

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Question 595929: There are22 more sophomores than juniors in an 8 am algebra class. If there are 70 students in this class, find the number of sophomores and the number of juniors in the class.
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Question 596202: Suppose that 13% of the voters in a state intend to vote for a certain candidate. What is the probability that a survey polling nine people reveals that three or fewer intend to vote for that candidate? (Round your answer to 4 decimal places.)

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Question 596214: A die is rolled 15 times. What is the probability of at least two 5's appearing?
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Question 596216: Sixty percent of a particular model of car are silver. What is the probability that in the next 10 observations of this model you observe 5 silver cars? (Round your answer to four decimal places.)

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Question 487804: d. There are 200 students in a sample. How many of these students will have scores that fall under the score of 41? Mean=45 standard deviation=4
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Question 596269: a coin is tossed 5 times find the probability of at most 4 tails. use combination formula
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Question 596250: Part 1 convert the fraction 7/10th to equivalent percentage?
Part 2 Then convert 54.2 to equivalent decimal?
Part 3 What is 77% of 500?
Part 4 convert .686 to a equivalent percentage?

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Question 596286: Please help me to find the correct answers at this question:
The diagram at right illustrates the logic of hypothesis testing. Note that in the diagram, type I error has been labeled as Be sure in your answer to identify:
a. curve 1
b. curve 2
c. Area A
d. Area B
e. Area C.
Short calculation Questions:

Also, here is the graph, I think that you could see it.
Thank you very much, Tutors make a great job.

Click here to see answer by Alan3354(30993) About Me 

Question 596348: This is a Normal Probability Distribution problem. Can I get some step by step help in solving this problem so I can try solving the other problems by myself. I am really having a hard time. Thank you so much.
The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces.
a. What percentage of all cans produced contain more than 8.4 ounces of tomato paste?
b. What percentage of all cans produced contain less than 7.8 ounces?
c. What percentage of cans contains between 7.4 and 8.2 ounces?
d. Ninety-five percent of cans will contain at least how many ounces?
e. What percentage of cans contains between 8.2 and 8.4 ounces?

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Question 596335: A. In a pole 48% of 830 surveyed adults that pesticides are very harmful what is the actual number of adults that said that pesticides are very harmful?
B. among the 830 surveyed adults 139 said that pesticides are not at harmful what are the percentages who chose not at al harmful?

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Question 596322: Hello there, I need your help on probability-tree diagram. I'm very thankful if anyone could help me on this. Thanks!
In a class, the probability that a student wears a watch is 0.8. Three students are randomly selected from the class.
(A) Draw a tree diagram showing all posible outcomes and their probabilities.
(B) What is the probabilty that
(i) all three students wear a watch
(ii) only te first three student wears a watch
(iii) only one student does not wear a watch
(iv) none of the three student wears a watch

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Question 596219: Fifteen percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors.
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Question 596421: suppose a mathematician has a 9/10 probability of answering any math questions correctly. What is the probability that he answers exactly 3 out of 5 math questions correctly
a. 0.0081
b. 0.0729
c. 0.54
d. 0.328
find the geometric means in the following sequence.
48, ?,?,?,?, -25815552
a. -13440,-20160,-26880,-33600
b. -672,9408,-131712,1843968,
c. 672,9408,131712,1843968,
d. 9408,-131712,1843968,-25815567

Click here to see answer by stanbon(57314) About Me 

Question 596061: A die is rolled 100 times with the following results.
Outcome-1 2 3 4 5 6
Frequency-25 18 12 23 14 8
Compute the empirical probability that the die comes up 2 or 3.

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Question 596704: alan tosses a nickel and rolls a number cube. What is the total possible outcomes fo these events?
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Question 596677: If someone has a stack of cards numbered 1-25 , what is the experimental probability of getting a card divisible by 6?
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Question 596785: Historically, 9 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database.

a. What is the probability that none of the next 16 repeat customers who call will have an incorrect address?
b. What is the probability that five customer who call will have an incorrect address?
c. What is the probability that six customers who call will have an incorrect address?
d. What is the probability that fewer than seven customers who call will have an incorrect address?
All answers should be rounded to four decimal places.


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Question 596859: If you are dealt three cards from a shuffled deck of 52 cards, what is the probability that all three cards are face cards.
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Question 596565: let a and b be events such that p(a) = 1/7, p(a or b)=1/2 and p(a and b)=1/10
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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, 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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, 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