The percent of calories from a fat person in America consumes each day is normal

Question

The percent of calories from a fat person in America consumes each day is normally distributed with a mean of 41 and a standard deviation of 7. Suppose a person is selected at random. Let X=percent of calories from fat 6. The percent of calories from fat a person in America consumes each day is normally distributed with a mean of41 and a standard deviation of 7. Suppose a person is selected at random. Let X-percent of calories from fat. Find the probability that the percent of calories a person consumes from fat is greater than 45 Find the probability that the percent of calories a person consumes from fat is between 40 and 50. b. c. d. If 16 people were selected, find the probability chat the mean percent of calories consumes from e. Find the maximum number of calories from fat a person in the first quartile consumes each day. fat is less than 30. f. What is the minimum number of calories from fat consumed by a person in the top 25 percent?

Explanation / Answer

Answer to the question is as follows:

6.

a. X~N(41,7)

b. P(X>45) = P(Z> 45-41/7) = .2839

c. P(40<X<50) = P(40-41/7 <Z< 50-41/7) = P(-1/7 <Z< 9/7) = 0.7162-0.4432 = 0.2730

d. n = 16, P(X<30 ) = P(Z< (30-41)/(7/sqrt(16)) = ~0

e. P(X<=c) = .25
(c-41)/7 = -.675
= -.675*7+41 = 36.275

f. P(X>=c) = .25
(c-41)/7 = +.675
= +.675*7+41 = 45.725

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