Question

A subset of 18- to 25- year old workers have some extra money to burn and are called "gold-collar" workers. These workers are spending an average of $729 per month on themselves (versus $267 for college students and $609 for "blue collar" workers). Assuming this spending is normally distributed with a standard deviation of $92.00, what percentage of gold-collar workers spend:

a.) Between $400 and $1000 a month on themselves

b.) Less than $500 a month on themselves

Answer 1

(a)

= 729

= 92

To find P(400 < X < 1000):

Case 1 : For X from 400 to mid value:

Z = (400 - 729)/92 = - 3.5761

Table of Area Under Standard Normal Curve gives area = 0.4998

Case 2: For X from mid vale to 1000:

Z = (1000 - 729)/92 = 2.9457

Table gives area = 0.4984

So,

P(400 < X < 1000) = 0.4999 + 0.4984 = 0.9983 = 99.83 %

(b)

To find P(X<500):

Z = (500 - 729)/92 = - 2.4891

Table gives area = 0.4936

So,

P(X<500) = 0.5 - 0.4936 = 0.0064 = 0.64 %