Question

The life of Sunshine CD players is normally distributed with a mean of 4.7 years and a standard deviation of 1.2 years.1. We are interested in the length of time a CD player lasts. a. Find the probability that a CD player will break down during the guarantee period. P(0<x<____) = _______.

b. Sketch and shade a normal curve to indicate the probability we are interested in. Be sure to label and scale the horizontal axis. c. Some CD players last up to 6 years.

d. Find the probability that a CD player will last between 2.75 and 6 years. e. Sketch and shade a normal curve as in question 1.b.

Answer 1

Mean, M = 4.7

Standard Deviation, S = 1.2

a) P(X<4.7) is required

Below the mean, we have exactly half of the area in the normal curve

So, P(X<4.7) = 0.5

b) We are interested in the area to the left of the mean, the left half of normal curve

c) Some CD players last up to 6 years

P(X<6) is required

Z-score = (X-M)/S = (6-4.7)/1.2 =1.083

P(Z<1.083) = 0.8599

d) The probability that a CD player will last between 2.75 and 6 years

P(2.75<X<6) is required

Z-score for X=2.75 is (X-M)/S = (2.75-4.7)/1.2 = -1.625

Z-score for X= 6 is (X-M)/S = (6-4.7)/1.2 =1.083