Question

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. a.) TRUE or FALSE: The random variable is defined as the average percent of fat calories consumed each day by a person in America. b.) For a sample of size 16, state the mean of the sample mean. c.) For a sample of size 16, state the standard deviation of the sample mean (the "standard error of the mean"). d.) Suppose a sample of size 16 is taken. Find the probability that the average percent of fat calories consumed is more than 30.

Answer 1

Solution:

Given that,

= 36

= 10

n = 16

So,

= 36

a ) True

b )   =  ( / )

c ) = (10 / 16)

d ) = 2.5

p (   > 30)

= 1 - p (   < 30)

= 1 - p ( - /) < (30 - 36 / 2.5)

= 1 - p ( z < - 6 / 2.5 )

= 1 - p ( z < -2.4)

Using z table

= 1 - 0.0082

= 0.9918

Probability = 0.9918