Question

For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.

A. 0.4082
B. 0.4025
C. 0.4213
D. 0.4156

Answer 1

A. 0.4082

Explanation:

According to the given data

mean 'μ' =50

standard deviation 'σ'=15

In order to find the probability for 50<x<70 , we use the standard form

Z= (x−μ) /σ

​

when x=50, Z will be zero

therefore, Z=0

when x=70,

Z=(70−50)/15

Z= 20/15

Z=1.33

next is to find the probability for 50<x<70

for standard form 0<z<1.33

By using Z-table, the area is equal to 0.4082

Thus, probability that the length of time will be between 50 and 70 hours is 4082