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

Tutors Answer Your Questions about Probability-and-statistics (FREE)

Question 220875: In how many distinct ways can an 18-digit number be made using nine 9's and nine 9's?
Click here to see answer by Alan3354(31532)

Question 220872: There are 26 chocolates in a box, all identically shaped. There are 7 filled with nuts, 9 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row?
Click here to see answer by checkley77(12569)

Question 220883: In a class of 50 students, 27 are democrats, 9 are business majors, and 6 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major?
Click here to see answer by stanbon(57977)

Question 220881: You are dealt one card from a 52 card deck. The the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of getting a picture card the first time and a club the second time?
Click here to see answer by stanbon(57977)

Question 220877: 1.Past history reveals that 30% of students who enroll in an online course drop the course before the last day to withdraw without penalty. Answer the following questions for an online class with a beginning enrollment of 20 students.
F.Find the probability that 4 – 8 items students will drop the course
g.Write out the exact Excel function that could be used to answer question f.

Click here to see answer by stanbon(57977)

Question 220856: what is the critical value zc necessary to form a confidence interval at the given level of confidence 85%
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Question 221038: A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?
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Question 221022: A standard placement test has a mean of 105 and a standard deviation of σ = 13. Determine the minimum sample size if we want to be 99% certain that we are within 3 points of the true mean
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Question 221107: Let X be a normal random variable with mean 20 and standard deviation 4. Find P(X < 19).
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Question 221110: The sum of the digits of a number is 9. What is the probability that the number is prime?
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Question 221110: The sum of the digits of a number is 9. What is the probability that the number is prime?
Click here to see answer by jim_thompson5910(28717)

Question 221102: Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds in favor of drawing an ace and a king?
Click here to see answer by checkley77(12569)

Question 221123: Suppose that the mean score of a class of 28 students was 74. The 18 male students in the class had a mean score of 66. What was the mean score for the 10 female students?
I don't understand how to find this answer.
Click here to see answer by stanbon(57977)

Question 220936: Please show calculation to problem. Dullco Manufacturing claims that its akaline batteries last forty hours on average in a certain type of portable CD player. Tests on a random sample of 18 batteries showed a man battery life of 37.8 hours with a standard deviation of 5.4 hours. What is the test statistic? In a left-tailed test at a = .05 would we rejecting the claim, accepting the claim, either cause it is too close,or switch to a = .01 for a more powerful test.
Click here to see answer by stanbon(57977)

Question 221362: Can somebody pretty please solve this problem for me and explain how to get to the answer?
Grace has 16 jelly beans in her pocket. She has 8 red ones, 4 green ones and 4 blue ones. What is the minimum number of jelly beans she must take out of her pocket to ensure that she has one of each colour?
Thanks (:
Click here to see answer by stanbon(57977)

Question 221501: : (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
1. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?
How do I find the decision rule?
Click here to see answer by stanbon(57977)

Question 221659: 2. How many 4-character license plates are possible with 2 letters from the alphabet followed by 2 digits, if repetitions are allowed? if repetitions are not allowed?
Click here to see answer by stanbon(57977)

Question 221674: The new Twinkle bulb has a standard deviation 34 hours. A random sample of 77 light bulbs is selected from inventory. The sample mean was found to be 492 hours. Find the margin of error E for a 90% confidence interval. Round your answer to the nearest hundredths. Then I have to construct a 90% confidence interval for the mean life. I know how to do that part I just can't figure out the first part. The sqrt gets me.
Click here to see answer by stanbon(57977)

Question 221683: Your favorite pizza parlor offers six meat toppings and eight veggie toppings. If you order a three-topping pizza at random, what is the probability that it is vegetarian?
14 toppings offered, so n = 14
Arrange in groups of 3, so r = 3
n!/r!(n-r)!
14!/3!(14-3)! = 364 possible combinations

Click here to see answer by josmiceli(9817)

Question 221673: A resturant offers salads with 8 different types of dressings and 4 different toppings. How many different salads are available?
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Question 221737: Compute the following: 3! ÷ (0! * 3!)
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Question 221752: an urn contains 4 red, 2 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?
Click here to see answer by jsmallt9(3296)

Question 221782: In city A, it is known that the mean monthly energy usage per household has historically been 1,570 kilowatt-hours per month. The population standard deviation in monthly household energy use is not known.
Recently, there has been a widespread government campaign using print, radio and television media aimed at encouraging household to be more energy efficient.
As part of investigating the success of the campaign, research was commissioned to study the possible effect on average household energy usage. A sample of 56 randomly selected households had their monthly energy use measured for a period before and after the campaign. The researcher will use the before and after measurements, corresponding to each household, to test the hypothesis that the mean difference in household energy use before and after the campaign is more than zero. They will use a level of significance of 0.01.
Select the correct null and alternate hypotheses for this test:

1.)H0: μd = 0
H1: μd ≠ 0

2.)H0: μd ≠ 0
H1: μd = 0

3.)H0: μd ≤ 0
H1: μd > 0

4.)H0: μbefore - μafter ≠ 0
H1: μbefore - μafter = 0

5.)H0: μbefore - μafter = 0
H1: μbefore - μafter ≠ 0

6.)H0: μd > 0
H1: μd ≤ 0
Click here to see answer by stanbon(57977)

Question 221781: Dr Carl is a mathematics and statistics lecturer. He is interested in studying a new approach at teaching mathematics and statistics in high school. Recently this new approach has been adopted.
It was previously the case that the mean score for all high school students doing their end of year exam was 68, however, the population standard deviation is unknown. The scores of all students are approximately normally distributed.
He thinks that, with this new teaching approach, the mean score may have increased.
A random sample of 50 scores is gathered and the sample mean and standard deviation calculated.
Dr Carl will conduct a hypothesis test using a level of significance of 0.05.
Select the correct null and alternate hypotheses for this test:

a.)H0: μ > 68
H1: μ ≤ 68

b.)H0: μ ≤ 68
H1: μ < 68

c.)H0: μ = 68
H1: μ ≠ 68

d.)H0: μ ≤ 68
H1: μ > 68
Click here to see answer by stanbon(57977)

Question 221780: Heather is a student in a class that has been asked to conduct a hypothesis test for a population proportion. The null and alternative hypotheses are:
H0: Pi symbol = 0.5
H1: Pi symbol ≠ 0.5
Heather is given a sample and calculates the test statistic. Using a level of significance of α = 0.05, she rejects the null hypothesis. Heather's friends, Alan and Bill, also use the sample to calculate a test statistic. However, they differ in the level of significance they use. Alan uses a level of significance of α = 0.1, while Bill uses α = 0.01. All three students perform their calculations correctly.
For each of Heather's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given.
Reject Retains Cannot tell
a) Alan
b) Bill
Click here to see answer by stanbon(57977)

Question 221778: A teacher is interested in comparing the means scores on a mathematics and verbal test for two populations of students, population A and population B. In particular, the teacher suspects that the mean score for population A is higher than in population B.
A random sample of 30 test scores from each population is collected.
Sample A
83.5 66 92.5 61.5 62.5 94
71.5 68 97 66.5 93 71.5
63 90.5 69 93 95 66
74 92.5 85 66.5 86.5 65
73 66.5 88.5 69.5 80 69.5

Sample B
92 51.5 73 73 95 63
74 79 46.5 93.5 88 88
64.5 49.5 79 51.5 53 89.5
78.5 84.5 80 72.5 71 94.5
67 55 85.5 70 92 64.5
Conduct a one-tailed hypothesis test for equality of the populations means.
You may find this Student's t distribution table useful.
a)Calculate the test statistic. Give your answer to 3 decimal places.
t =???
b)At a 95% confidence level, from the result of the test you can conclude that there is:
1.)significant evidence to conclude that the mean of population A is greater than the mean of population B
2.)significant evidence to conclude that the mean of population A is less than or equal to the mean of population B
3.)not enough evidence to conclude that the mean of population A is greater than the mean of population B
4.)not enough evidence to conclude that the mean of population A is less than or equal to than the mean of population B
Click here to see answer by stanbon(57977)

Question 221779: A climate researcher knows that it has previously been the case that the mean temperature in his city has been 23.9 °C. He suspects that this may no longer be the case and that the mean temperature may now have changed, and he suspects that is has risen in recent times. He collects sample data with the aim of conducting a hypothesis test to examine his suspicions. He will use a level of significance of 0.01 for the test.
Select the correct null and alternate hypotheses for this test:

a.)H0: μ ≠ 23.9 °C
H1: μ = 23.9 °C

b.)H0: μ ≤ 23.9 °C
H1: μ > 23.9 °C

c.)H0: μ = 23.9 °C
H1: μ ≠ 23.9 °C

d.)H0: μ > 23.9 °C
H1: μ ≤ 23.9 °C
Click here to see answer by stanbon(57977)

Question 221801: Fsu wants to make an inference about the percentage of students at the school who perfer having a break between the last day of school and the start of exams to help reduce stress. a survery is taken of 1000 students.
- it is known that the population proportion that favor a break between classes and final exams is 50%. let the random variable x be defined as the number of students that are in favor of a break between classes and final exams. state the distrubtion if x and compute the mean and variance of the distrubtion????
Click here to see answer by stanbon(57977)

Question 221751: an urn contains 4 red, 2 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?
Click here to see answer by stanbon(57977)

Question 221915: Manu and Janani are playing a coin toss game with a fair penny. Manu gets a point if the penny lands on heads, and Janani gets a point if the penny lands on tails. The score is Janani 9, Manu 7, in a game to 10 points. What is the probability that Janani will win the game? Express your answer as a common fraction.
Click here to see answer by solver91311(17077)

Question 221887: It is asserted that 90 percent of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of six cars:
At least four will have the transponder. (Round your answer to 4 decimal places.)
Probability :

Click here to see answer by stanbon(57977)

Question 222240: What is the probability that a randomly selected person in the town is a Republican or a Democrat?
Click here to see answer by stanbon(57977)

Question 222179: You have a traffic light of only a red and a green light. What is the probability that you will get 2 green lights out of 4 times the light changes?
I figured that probability of one try is .5. It is either green or red the 1st time. Then I wrote out the possibilities of 2 light changes, and came up with rr, rg, gr, gg. (So 2 greens is 1/4, or .5 x .5 = .25.) After this, I am stuck. I don't think it's .5 x .5 x .5 x .5. That would be too small a probability. I think the events are independent and mutually exclusive, but then I don't know what to do. My dad and I tried to write out all the possibilities, and got 16 of them, with 6 times getting 2 greens, so that would be 6/16 or 3/8, but we're not sure. We did not count the cases where we got 3 or 4 greens... do you count those too? And I don't have a good formula to go by... if the problem were 9 tries or something, I'd never figure it out!
Click here to see answer by stanbon(57977)

Question 222354: The historical mean for fish caught at a certain Florida lake is 10 pounds with a standard deviation of 1.2 pounds. A fishman goes on a Satuday and catches 12 fish whhich had a mean weight of 11 pounds. Has themean weight of fish at the Florida lake increased? Use a = .05 Please show calculation to problem.
Click here to see answer by stanbon(57977)

Question 222376: How many ways can 8-toppings be selected to make three-topping pizzas?
Click here to see answer by jim_thompson5910(28717)

Question 222378: There are 7 black, 10 blue, 2 red, and 1 yellow marbles. What is the probability of selecting a black marble and then a blue marble if the marbles are replaced?
What is the probability if the marbles are not replaced?
Click here to see answer by stanbon(57977)

Question 222468: find the twelfth term of the geometric sequence: 1/16, 1/8, 1,4...
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Question 222475: how many ways can 9 keys be arranged on a circular key ring?
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Question 222476: what is the probability of getting an even number on a single roll of a number cube if you roll a 3 or greater
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Question 222483: the probability of being named captain of the basketball team is 1/5.what are the odds of being named captain of the team?
Click here to see answer by stanbon(57977)

Question 222495: find the probability of tossing exactly 2 heads on 3 tosses of a fair coin.
Click here to see answer by stanbon(57977)

Question 222511: find the 50th term in the arithmetic sequence 1,5,9,....
Click here to see answer by drj(1380)

Question 222509: two cards are drawn at random from a standard deck of 52 cards.what is the probability that both cards are queens?
Click here to see answer by rfer(12730)

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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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, 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