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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Sample score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex]
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.
[tex]-2=\frac{1000-1200}{\sigma}[/tex]
[tex]-2=\frac{-100}{\sigma}[/tex]
[tex]\sigma=\frac{-100}{-2}[/tex]
[tex]\sigma=50[/tex]
We can use sample score 1300 and get same answer as:
[tex]2=\frac{1300-1200}{\sigma}[/tex]
[tex]2=\frac{100}{\sigma}[/tex]
[tex]\sigma=\frac{100}{2}[/tex]
[tex]\sigma=50[/tex]
Therefore, the standard deviation of the light bulbs’ life is 50 years.
