A population has a mean of 50 and a standard deviation of 6. (a) What are the

mean and standard deviation of the sampling distribution of the mean for N =

16? (b) What are the mean and standard deviation of the sampling distribution of

the mean for N = 20?

2. Given a test that is normally distributed with a mean of 100 and a standard

deviation of 12, find:

a. the probability that a single score drawn at random will be greater than 110

b. the probability that a sample of 25 scores will have a mean greater than 105

c. the probability that a sample of 64 scores will have a mean greater than 105

d. the probability that the mean of a sample of 16 scores will be either less than

95 or greater than 105

3. What term refers to the standard deviation of a sampling distribution?

4. (a) If the standard error of the mean is 10 for N = 12, what is the standard error

of the mean for N = 22? (b) If the standard error of the mean is 50 for N = 25,

what is it for N = 64?

5. A questionnaire is developed to assess women's and men's attitudes toward

using animals in research. One question asks whether animal research is wrong

and is answered on a 7-point scale. Assume that in the population, the mean for

women is 5, the mean for men is 4, and the standard deviation for both groups is

1.5. Assume the scores are normally distributed. If 12 women and 12 men are

selected randomly, what is the probability that the mean of the women will be

more than 2 points higher than the mean of the men?

6. If the correlation between reading achievement and math achievement in the

population of fifth graders were 0.60, what would be the probability that in a

sample of 28 students, the sample correlation coefficient would be greater than

0.65?

If numerous samples of N = 15 are taken from a uniform distribution and a

relative frequency distribution of the means is drawn, what would be the shape of

the frequency distribution?

8. A normal distribution has a mean of 20 and a standard deviation of 10. Two

scores are sampled randomly from the distribution and the second score is

subtracted from the first. What is the probability that the difference score will be

greater than 5? Hint: Read the Variance Sum Law section of Chapter 3.

9. What is the shape of the sampling distribution of r? In what way does the shape

depend on the size of the population correlation?

10. If you sample one number from a standard normal distribution, what is the

probability it will be 0.5?

11. A variable is normally distributed with a mean of 120 and a standard deviation

of 5. Four scores are randomly sampled. What is the probability that the mean

of the four scores is above 127?

12. The correlation between self-esteem and extraversion is .30. A sample of 84 is

taken. a. What is the probability that the correlation will be less than 0.10? b.

What is the probability that the correlation will be greater than 0.25?

13. The mean GPA for students in School A is 3.0; the mean GPA for students in

School B is 2.8. The standard deviation in both schools is 0.25. The GPAs of

both schools are normally distributed. If 9 students are randomly sampled from

each school, what is the probability that:

a. the sample mean for School A will exceed that of School B by 0.5 or more?

b. the sample mean for School B will be greater than the sample mean for

School A?

14. In a city, 70% of the people prefer Candidate A. Suppose 30 people from this

city were sampled.

a. What is the mean of the sampling distribution of p?

b. What is the standard error of p?

5. (4 points each) The chair of the Department of Mathematics and Statistics needs to appoint a faculty committee consisting of 5 mathematics and 6 statistics faculty. There are 20 mathematics and 15 statistics faculty members in the department. (a) In how many ways can he select such a committee? (Note: set up a numerical expression using fractions, factorials, and binomial coefficients as necessary; you don't have to evaluate it./ (b) What is the probability that randomly selected 11 people will actually form such a committee? Note: Set up a numerical expression using fractions, factorials, and binomial coefficients as necessary; you don't have to evaluate it./4. [8 marks] 60 % of students who apply to do a masters in statistics have an undergraduate degree in statistics, 25% have an undergraduate degree in mathematics, and 15% an undergraduate degree is a program other than statistics or mathematics. The acceptance percentage is 85%, 75%, and 60% for statistics, mathematics, and other degree respectively. A. [1.5] If an applicant is randomly selected, what is the probability he/she has a degree in mathematics and got accepted? B. [2.5] If an applicant is randomly selected, what is the probability he/she didn't get accepted? C. [4) If an applicant is randomly selected and was found to be accepted, what is the probability he/she has an undergraduate degree from a program other than mathematics or statistics?Question: At a liberal arts college, 90% of the freshmen are enrolled in English 105, 80% are enrolled in Mathematics 101 and 5% are enrolled in Mathematics 101 but not in English 105. A freshman is randomly selected. a. What is the probability that the freshman is enrolled in both English 105 and Mathematics 101? b. What is the probability that the freshman is enrolled in English 105 but not in Mathematics 101? c. Suppose the freshman chosen is known to be enrolled in Mathematics 101. What is the probability that the freshman is also enrolled in English 105? P(E) = 0.90 P(M) = 0.80 m M P(MnE ) = 0.05 P(EnM') = 0.15 P(MnE) = 0.750.05 QUESTION 11 1.00000 points At a liberal arts college, 90% of the freshmen are enrolled in English 105, 80% are enrolled in Mathematics 101 and 5% are enrolled in Mathematics 101 but not in English 105. A freshman is randomly selected. What is the probability that the freshman is enrolled in English 105 but not in Mathematics 101? noljesup 0.90 O 0.80 O 0.75 0.15 0.05