Question

Weekly fast food expenditures by young adults are normally distributed with a mean of $42.85 and a standard deviation of $12.35.

A) What is the probability that a randomly selected young adult will spend more than $47 weekly on fast food? Round to four places after the decimal point.

B) Young adults in the bottom 4% of weekly expenditures on fast food are designated as FFF. What money amount represents the maximum weekly expenditures for FFF young adults? Round to two places are the decimal point.

Answer 1

Given,

= 42.85 , = 12.35

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X > 47) = P( Z > 47 - 42.85 / 12.35)

= P( Z > 0.3360)

= 1 - P( Z < 0.3360)

= 1 - 0.6316

= 0.3684

b)

We have to calculate x such that P( X < x) = 0.04

That is

P( Z < x - / ) = 0.04

From Z table, z-score for the probability of 0.04 is -1.7507

So,

x - / = -1.7507

Put the values of and in above equation and solve for x

x - 42.85 / 12.35 = - 1.7507

x = 21.23