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?

Suppose you take 50 measurements on the speed of cars on Interstate 5, and

that these measurements follow roughly a Normal distribution. Do you expect

the standard deviation of these 50 measurements to be about 1 mph, 5 mph, 10

mph, or 20 mph? Explain.

28. Suppose that combined verbal and math SAT scores follow a normal

distribution with mean 896 and standard deviation 174. Suppose further that

Peter finds out that he scored in the top 3% of SAT scores. Determine how high

Peter's score must have been.

29. Heights of adult women in the United States are normally distributed with a

population mean of ?= 63.5 inches and a population standard deviation of ? =

2.5. A medical re- searcher is planning to select a large random sample of adult

women to participate in a future study. What is the standard value, or z-value,

for an adult woman who has a height of 68.5 inches?

30. An automobile manufacturer introduces a new model that averages 27 miles

per gallon in the city. A person who plans to purchase one of these new cars

wrote the manufacturer for the details of the tests, and found out that the

standard deviation is 3 miles per gallon. Assume that in-city mileage is

approximately normally distributed.

a. What is the probability that the person will purchase a car that averages less

than 20 miles per gallon for in-city driving?

b. What is the probability that the person will purchase a car that averages

between 25 and 29 miles per gallon for in-city driving

7 Exercise 7 In a certain college, 25% of the students failed mathematics, 15% failed chemistry and 10% failed both mathematics and chemistry. A student is selected at random. a) Dene the two relevant events. b) If the student failed chemistry, what is the probability that he failed mathematics? (3) If the student failed mathematics, what is the probability that he failed chemistry? (1) What is the probability that the student failed mathematics or chemistry e) What is the probability that the student failed neither mathematics nor chemistry? 0.05 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 0.05A survey of 200 students is taken. It was found that 50% were studying Accounting, 30% Economics, and the rest were studying Statistics. It was also found that 51% were male. Among the male students, 35% were in Accounting, 40% were in Economics, and the rest were in Statistics. a. What is the probability of student is female and studying Statistics? b. What is the probability of randomly selected student who is found to be a Statistics major, being female? C. What is the probability that a student is male or studying Economics? d. What is the probability that a student is studying Accounting if she is known to be female?help againi please due in 20 mins At a certain college, 82% of all students take Statistics, and 619% of all students take Economics. 559% of all students take both Statistics and Economics. P(9) = P(E) = Select an answer PIS or B) PIS and B) P(B) PIS] = 0.55 To decide, we have to calculate Select an answer P(B) PIS] P(S or B) P(S and E) which in this problem is equal to . We conclude that $ and E are Select an answer mutually exclusive not mutually exclusive , because Select an answer PIS and E) is equal to 0 PIS and E] is not equal to 0 P(S or E) is not equal to 0 P(S or E) is equal to 1. Let S be the event that a student takes Statistics. Let E be the event that a student takes Economics. Summarize in symbols the probabilities described above. 2. Find the probability that a randomly selected student does not take Statistics. 3. Find the probability that a randomly selected student does not take Economics 4. Find the probability that a randomly selected student takes Statistics or Economics. 5. Determine if the events, taking Statistics and taking Economics, are mutually exclusive. Explain