Question

Suppose a brand of light bulbs is normally​ distributed, with a mean life of 1400 hr and a standard deviation of 150 hr. Find the probability that a light bulb of that brand lasts between 1175 hr and 1610 hr.

Answer 1

Answer:

The probability that a light bulb of that brand lasts between 1175 hr and 1610 hr is 0.8524.

Step-by-step explanation:

Given : Suppose a brand of light bulbs is normally​ distributed, with a mean life of 1400 hr and a standard deviation of 150 hr.

To find : The probability that a light bulb of that brand lasts between 1175 hr and 1610 hr ?

Solution :

Applying z-score formula,

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

where, $\mu=1400$ is population mean

$\sigma=150$ is standard deviation

For x=1175 hour,

$z=\frac{1175-1400}{150}$

$z=\frac{-225}{150}$

$z=-1.5$

For x=1610 hour,

$z=\frac{1610-1400}{150}$

$z=\frac{210}{150}$

$z=1.4$

The required probability is,

$P(1175< X$

$P(1175< X$

Using z table, the values are

$P(1175< X$

$P(1175< X$

The probability that a light bulb of that brand lasts between 1175 hr and 1610 hr is 0.8524.