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Chapter 6: Q.6.57 (page 388)

The life of Sunshine CD players is normally distributed with a mean of 4.1years and a standard deviation of 1.3years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period.

a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.

b. P(0<x<____________)=___________(Use zero for the minimum value of x.)

Short Answer

Expert verified
  1. The graph for the P(0<x<3)is

b. The value of theP(0<x<3)is0.1979.

Step by step solution

01

Given information (Part a)

Given in the question that

Mean=4.1

Standard deviation=1.3

02

Solution (Part a)

The graph for the P(0<x<3)with the shaded region is given below

03

Given information (Part b)

Given in the question that

Mean=4.1

Standard deviation=1.3

04

Solution (Part b)

Here we need to calculate the probability is below,

P(0<x<3)=P(x<3)鈭�P(x<0)

=Px鈭�渭蟽<3鈭�渭蟽鈭�Px鈭�渭蟽<0鈭�渭蟽

=PZ<3鈭�4.11.3鈭�PZ<0鈭�4.11.3

=P(Z<鈭�0.8462)鈭�P(Z<鈭�3.1538)

=0.1987鈭�0.0008From standardnormal table

=0.1979

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