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Name: _____________________________________________________________ Date: _____________________ 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?