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

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 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories. Round all answers to two decimal places.

A. X ~ N( ____ , ____ )

B. Find the probability that a randomly selected fat calorie percent is more than 41.

C. Find the minimum number for the upper quarter of percent of fat calories.

D. Write the probability statement. (Round your answer to two decimal places.)

Approximately 25% of people consume ____ than ___ % of their calories as fat.

Explanation / Answer

a)  X ~ N( 36 ,10 )

b) mean = 36 , std.deviation = 10

p(x >41)

z = ( x - mean ) / s

= ( 41 - 36 ) / 10

= 0.5

Now, we need to find p(z > 0.5)

p (x >41 ) = p (z >0.5) = 0.31

c) for upper quarter we have z value = 0.674

z = ( x - mean ) / s

0.674 = ( x - 36) / 10

x = 42.74

d)

Approximately 25% of people consume _greater than 42.74% of their calories as fat.

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