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?