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1. According to the U.S. Department of Agriculture, the mean calorie intake of m

ID: 3321431 • Letter: 1

Question

1. According to the U.S. Department of Agriculture, the mean calorie intake of males aged 20 to 39 yea! in U.S. is p=2716, with standard deviation o= 72.8. Suppose that the calorie intake of males age to 39 years in U.S. follows normal distribution. (A) What percent of males aged 20 to 39 years in U.S. approximately take 2730 calories or higher? (O points) (B) What is the probability that the sample mean from a random sample of size 40 males aged 20 to 39 years in U.S. would result in a sample mean of 2730 calories or higher? (7 points)

Explanation / Answer

A) (P(X > 2730)

= P((x - mean)/SD > (2730 - mean)/SD)

= P(Z > (2730 - 2716)/72.8)

= P(Z > 0.19)

= 1 - P(Z < 0.19)

= 1 - 0.5753 = 0.4247 = 42.47%

B) (P(X > 2730)

= P((x - mean)/(SD/sqrt(n) > (2730 - mean)/(SD/sqrt(n))

= P(Z > (2730 - 2716)/(72.8/sqrt(40))

= P(Z > 1.22)

= 1 - P(Z < 1.22)

= 1 - 0.8888 = 0.1112