3. A statistical analysis of 1,000 long-distance telephone calls made from the h

Question

3. A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Delaware Compüter Corporation indicates that the length of. these calls is normally distributed, with mean 240 seconds and standard deviation= 40 seconds. a. What percentage of these calls lasted less then 180 seconds? b. What is the probability that a particular call lasted between 180 and 300 seconds? c. How many calls lasted less than 180 seconds or more than 300 seconds? d. What percentage of the calls lasted between 110 and 180 seconds?

Explanation / Answer

Result:

3.

a).

z value for 180, z =(180-240)/40 = -1.5

P( x < 180) = P( z < -1.5) =0.0668

The required percentage =6.68%

b).

z value for 300, z =(300-240)/40 = 1.5

P( 180<x <300) =P( -1.5<z<1.5)

=P( z<1.5) – P( z < -1.5)

=0.9332-0.0668

=0.8664

c).

P( x<180 or x >300) = 1- P( 180<x <300)

=1-0.8664 =0.1336

The required calls = 1000*0.1336 =133.6

=134

d).

z value for 110, z =(110-240)/40 = -3.25

P( 110<x <180) =P( -3.25<z<-1.5)

=P( z<-1.5) – P( z < -3.25)

= 0.0668- 0.0006

=0.0662

The required percentage =6.62%

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