A study of long-distance phone clls made from General Electric Corporate Headqua

Question

A study of long-distance phone clls made from General Electric Corporate Headquarters in Fairfield, necticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.60 minutes and the standard deviation was 0.40 minutes. a. What fraction of the calls last between 3.60 and 4.20 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls b. What fraction of the calls last more than 4.20 minutes? (Round z-score computation to 2 decima places and your final answer to 4 decimal places.) Fraction of calls c. What fraction of the calls last between 4.20 and 5.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls d. What fraction of the calls last between 3.00 and 5.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls e. As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.) Duration

Explanation / Answer

(a) what fraction of the calls last between 3.60 and 4.20?

Ans:

Mean== 3.60 minutes
Standard deviation == 0.40 minutes
x1= 3.60 minutes
x2= 4.20 minutes
z1=(x1-)/

    =(3.60-3.60)/0.40

    =0
z2=(x2-)/

   =(4.20-3.60)/0.40

   =0.6/0.40

   =1.5
Cumulative Probability corresponding to z1= 0 is= 0.5 0r= 50.00%
Cumulative Probability corresponding to z2= 1.5 is= 0.93310r= 93.31%

Therefore probability that the value of x will be between x1= 3.60 and x2= 4.20
is =93.31%-50.%

    =43.31

Fraction of the call between 4.2 and 5.0 minutes= 0.4331 or 43.31%

(b) what fraction of the calls morethan 4.20 minutes?

      

Mean== 3.60 minutes
Standard deviation == 0.40minutes
x= 4.20
      z=(x-)/

=(4.20-3.60)/0.40

        =1.5
Cumulative Probability corresponding to z= 1.5 is= 0.9331
Therefore probability corresponding to x> 4.20 is 1-Prob(Z )=1-0.9331=0.0669
0r= 6.69%

Fraction of the calls greater than 4.20 minutes= 0.0669
0r= 6.69%

(C)

what fraction of the calls last between 4.20 and 5.00?

Ans:

Mean== 3.60 minutes
Standard deviation == 0.40 minutes
x1= 4.20 minutes
x2= 5.00minutes
z1=(x1-)/

    =(4.20-3.60)/0.40

    =0.6/0.40

   =1.5
z2=(x2-)/

   =(5.00-3.60)/0.40

   =1.4/0.40

   =3.5
Cumulative Probability corresponding to z1=1.5 is= 0.93310r= 93.31%

Cumulative Probability corresponding to z2= 3.5 is= 0.99970r= 99.97%

Therefore probability that the value of x will be between x1= 4.20 and x2= 5.00
is =99.97%-93.31%

    =6.66%

Fraction of the call between 4.2 and 5.0 minutes= 0.666 or 6.66%

(D)

what fraction of the calls last between 4.20 and 5.00?

Ans:

Mean== 3.60 minutes
Standard deviation == 0.40 minutes
x1= 3.00 minutes
x2= 5.00minutes
z1=(x1-)/

    =(3.00-3.60)/0.40

    =-0.6/0.40

   =-1.5
z2=(x2-)/

   =(5.00-3.60)/0.40

   =1.4/0.40

   =3.5
Cumulative Probability corresponding to z1=-1.5 is= 0.0668 0r= 6.68%

Cumulative Probability corresponding to z2= 3.5 is= 0.99970r= 99.97%

Therefore probability that the value of x will be between x1= 4.00 and x2= 5.00
is =99.97%-6.68%

    =93.29%

Fraction of the call between 4.0and 5.0 minutes= 0.9329 or 93.29%

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