Question

The mean life of a particular brand of light bulb is 1200 hours. If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs’ life?​
​a) 200
​b) 100
​c) 50
​d) 25
​e) 75

Answer 1

Answer:

c) 50

Step-by-step explanation:

We have been given that the mean life of a particular brand of light bulb is 1200 hours. About 95% of this brand of bulbs will last between 1100 and 1300 hours.

We will use z-score formula to solve our given problem.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{z-score}$,

$x=\text{Sample score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$

We know that 95% of data points lies within two standard deviation of mean, so 1100 will correspond to a z-score of -2 and 1300 will correspond to a z-score of 2.

$-2=\frac{1000-1200}{\sigma}$

$-2=\frac{-100}{\sigma}$

$\sigma=\frac{-100}{-2}$

$\sigma=50$

We can use sample score 1300 and get same answer as:

$2=\frac{1300-1200}{\sigma}$

$2=\frac{100}{\sigma}$

$\sigma=\frac{100}{2}$

$\sigma=50$

Therefore, the standard deviation of the light bulbs’ life is 50 years.