Question

A set of wrist watch prices are normally distributed with a mean of 767676 dollars and a standard deviation of 101010 dollars. What proportion of wrist watch prices are between 636363 dollars and 909090 dollars? You may round your answer to four decimal places. S

Answer 1

0.8224

Explanation:

Data

• mean: $76

• standard deviation, sd: $10

• first value of interest, x1: $63

• second value of interest, x2: $90

z-score for x1:

z1 = (x1 - mean)/sd = (63 - 76)/10 = -1.3

z-score for x2:

z2 = (x2 - mean)/sd = (90 - 76)/10 = 1.4

The proportion of wrist watch prices are between $63 and $90 is:

P(z1 < z < z2) = P(z < 1.4) - P(z < -1.3)

P(z < 1.4) = 0.9192 (see first picture attached)

P(z < -1.3) = 0.0968 (see second picture attached)

P(z1 < z < z2) = 0.9192 - 0.0968 = 0.8224