Week 3 Statistics

Question 17 options: Suppose a random variable, x, follows a Poisson distribution. Let μ = 3 every day, find the P(X ≤ 12) over a week. Round answer to 4 decimal places. Answer:

0.0245

Question 1 options: It is known that 20% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the probability that 5 or more of them have a high school diploma? (That is, find P(X ≥ 5) (round to 4 decimal places) Answer:

0.0328

A coin is flipped 30 times. What is the probability of getting exactly 15 heads? Round answer to 4 decimal places. Answer:

0.1445

The table of data obtained from WWW.BASEBALL-ALMANAC.COM shows hit information for four well known baseball players. Suppose that one hit from the table is randomly selected. NAME Single Double Triple Home Run TOTAL HITS Babe Ruth 1,517 506 136 714 2,873 Jackie Robinson 1,054 273 54 137 1,518 Ty Cobb 3,603 174 295 114 4,189 Hank Aaron 2,294 624 98 755 3,771 TOTALS 8,468 1,577 583 1,720 12,351 Find P(hit was made by Babe Ruth|The hit was a Triple).

0.233

Question 13 options: Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 48% 28% 24% What is the probability that a randomly selected part-time student at this college takes at more than 2 courses? (That is, find P(X > 2) Answer:

0.24

Question 9 options: Find the probability of rolling a sum of two dice that is more than 7. Round answer to 4 decimal places. Answer:

0.4167

Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X=x) 0.16 0.11 0.06 - 0.36 0.21

no

True or False: The following table represents a valid discrete probability distribution. x 1 2 3 4 5 P(X=x) 0.16 0.06 0.05 0.21 0.01

False

Question 11 options: Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 52% 28% 20% What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Answer:

0.48

Question 3 options: A coin is flipped 30 times. What is the probability of getting 15 or more heads? Round answer to 4 decimal places. Answer:

0.5722

In a box there are 4 red cards and 7 blue cards. The cards are well-shuffled. If you pick a card without looking at the box, what is the probability that you pick a blue card? (round to 3 decimal places) Answer:

0.636

Question 15 options: A bank gets an average of 8.5 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 4 or more customers at this bank in one hour. (That is, find P(X≥4)) (round to 4 decimal places) Answer:

0.9699

Suppose a random variable, x, follows a Poisson distribution. Let μ = 2.5 every minute, find the P(X ≥ 125) over an hour. Round answer to 4 decimal places. Answer:

0.9835

A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 4 or more customers at this bank in one hour. (That is, find P(X≥4)) (round to 4 decimal places) Answer:

0.9977

Question 16 options: If random variable X has a Poisson distribution with mean = 10, find the probability that X is at least 2. (That is, find P(X ≥ 2) (round to 4 decimal places)

0.9995

Question 4 options: If random variable X has a binomial distribution with n=9 and P(success) =p= 0.4, find the standard deviation of X. (round to 4 decimal places) Answer:

1.4697

Question 8 options: You have a club of fifteen people. You need to pick a president, treasurer, and secretary from the fifteen. How many different ways can you do this? Leave answer as whole number, do not include decimals or commas. Answer:

2730

Question 5 options: Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the variance. Round answer to 4 decimal places. Answer:

3.1875

In a recent study, the following data were obtained in response to the question, "Do you favor recycling in your neighborhood?" Yes No No Opinion Males 25 15 10 Females 30 10 10 If a person is picked at random, what is the probability that the person is either male or has no opinion regarding recycling?

3/5

If a menu has a choice of 5 appetizers, 4 main courses, and 2 desserts, then the sample space for all possible dinners has how many outcomes?

40