Probability & Statistics
S.D. of Sample Proportions & Means
Name_____________________
1. A Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television
per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20
children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the
number of hours they watch television will be greater than 26.3 hours.
2. Just before a referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict
whether the budget will pass. Suppose that the budget actually has the support of 52% of the voters.
What's the probability the newspaper's sample will lead them to predict defeat?
3. The average number of pounds of meat a person consumes a year is 218.4 pounds. Assume that the
standard deviation is 25 pounds and the distribution is approximately normal. If a sample of 40
individuals is selected, find the probability that the mean of the sample will be less than 224 pounds per
year.
4. A survey found that Americans generate an average of 17.2 pounds of glass garbage each year. Assume
the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of
55 families will be between 17 and 18 pounds.
5. Information on a packet of seeds claims that the germination rate is 92%. What's the probability that
more than 95% of the 160 seeds in the packet will germinate?
6. A candy company claims that 10% of the M&M's it produces are green. In a really large bag, the kids
found 500 candies. What's the probability that this bag contains more than 12% green?
7. The mean weight of 18-year-old females is 126 pounds, and the standard deviation is 15.7 pounds. If a
sample of 25 females is selected, find the probability that the mean of the sample will be greater than
128.3 pounds. Assume the variable is normally distributed.
8. The mean grade point average of the engineering majors at a large university is 3.23, with a standard
deviation of 0.72. In a class of 48 students, find the probability that the mean grade point average of the
students is less than 3.15.
9. The average age of accountants is 43 years, with a standard deviation of 5 years. If an accounting firm
employs 30 accountants, find the probability that the average age of the group is greater than 44.2 years
old.
10. A study found that 6% of the population do not eat steak. What’s the probability that less than 4 % of a
sample of 20 don’t eat steak?
11.
Answer the following using the set {2, 4, 6, 8} .
a.
List of all the possible samples of size 2 that can be drawn from this set. (Sample with
replacement)
b. Construct the sampling distributions of the sample means for sample size 2.
12. What are the properties of a sampling distribution of means?
13. What are the properties of a sampling distribution of proportions?
14. The duration of human pregnancies can be described by a normal distribution with a mean of 266 days
and a standard deviation of 16 days.
a. What percentage of pregnancies should last between 270 and 280 days?
b. At least how many days should the longest 25% of all pregnancies last?
c. Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women.
What’s the probability that the mean duration for his 60 patients will be less than 260 days?
15. State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed
limit.
a. What’s the probability that a randomly selected driver is exceeding the speed limit?
b. The police plan to set up a radar trap and check the speeds of 80 cars. What’s the probability
that more than 75% of them are exceeding the speed limit?
16. Grocery store receipts show that customer purchases have a skewed distribution with a mean of $32 and
a standard deviation of $20.
a. Explain why you cannot determine the probability that the next customer will spend at least
$40.
b. Can you find the probability that the next 50 customers will spend an average of at least $40?
If so, find it!
17. The following are the heights in a class of 25 first-graders.
34
38
39
42
37
39.5
41.2
40.3
36
44
39
34
39.7
37.2
38
40
41
38
36.5
35
35.5
34.7
36.8
39
41
a. Find a point estimate of the mean height for mean height of all first-graders.
b. Find a point estimate for the proportion of first-graders who are taller than 40 inches.
c. Find a point estimate for the median height for all first-graders.
d. Find a point estimate for the standard deviation in the heights of all first-graders.
18. An insurance company checks police records on 582 accidents selected at random and notes that
teenagers were at the wheel in 91 of them. Create a 95% confidence interval for the percentage of all
auto accidents that involve teenage drivers.
19. A May 2002 Gallup Poll found that only 8% of a random sample of 1012 adults approved of attempts to
clone a human. Create a 92% confidence interval for the percentage of all adults who approve of
attempts to clone a human.
20. In 1998 a San Diego reproductive clinic reported 49 births to 207 women under the age of 40 who had
previously been unable to conceive. Find a 94% confidence interval for the success rate at this clinic.
Would it be misleading for the clinic to advertise a 25% success rate? Explain.
21. A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is
based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence
did the pollsters use?