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

The correct option is A $0.4082$

Given,

$\mu =50$ (mean)

$\sigma =15$ (standard\ deviation)

find the probability for $50<x<70$

converting the problem in standard form

$Z=\frac{(x-\mu )}{\sigma }$

for $x=50$,

$Z=0$

for $x=70$,

$Z=(70-50)/15=1.33$

for finding the probability for $50<x<70$

In the standard form $0<z<1.33$

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