SOLUTION: A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal p

Question 1064887: A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 4.30 minutes and the standard deviation was 0.50 minutes.
a. What fraction of the calls last between 4.30 and 5.00 minutes?
b.What fraction of the calls last more than 5.00 minutes?
c.What fraction of the calls last between 5.00 and 6.00 minutes?
d.What fraction of the calls last between 4.00 and 6.00 minutes?
e.As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 3 percent of the calls. What is this time?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The z value is (x-mean)/sd
a. is probability z is between 0 and 1.4 or 0.4192.
b. is probability z is >1.4, which is 0.0808, the rest of half the curve.
c. Between 5 and 6 minutes is probability z is between 1.4 and 3.4, or 0.0804.
d. Between 4 and 6 minutes is probability z is between -.6 and 3.4 or 0.7254.
e. The longest 3% of calls is at z=+1.88, so that 1.88*0.5=(x-mean)=0.94.
That would be x=4.3+0.94=5.24 minutes or more.
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