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AP Statistics
7.3 Worksheet
1. Assume that the heights of men are normally distributed with a mean of 69 inches and a standard
deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean
height between 68 and 70 inches.
a. PROBLEM - Name the population and the sample.
b. CONDITIONS (need to check Rule of Thumb 1!)
c. DISTRIBUTION: Find the mean of the distribution and the standard deviation.
Draw the normal curve – label and shade
d. CALCULATION and CONCLUSION (interpret in the context of the problem)
2. Let X = the amount of soda pop in 355 mL bottle. From past experience, the variable X is known to have
a normal distribution with mean 355 mL and a standard deviation of 2 mL. What is the probability that
the average amount of soda in the bottles in a randomly selected 12 pack is less than 351.5 mL?
Interpret your final answer.
3. The average number of pounds of red meat that a person consumes each year is 196 with a standard
deviation of 22 pounds. If a sample of 50 individuals is randomly selected, find the probability that the
mean of the sample will be less than 200 pounds.
a. How do you know that a normal approximation can be used?
b. Find the probability that the mean of the sample will be less than 200 pounds.
4. Prices for sound-system receivers are normally distributed, with a mean μ = $625 and a standard deviation
σ = $150.
a.
What is the probability that a randomly selected receiver costs less than $700?
b.
You randomly select 10 receivers. What is the probability that their mean cost is less than $700?