Question

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 580 hours. Find the probability of a bulb lasting for at most 606 hours. Round your answer to four decimal places

Answer 1

Answer:

The probability of a bulb lasting for at most 606 hours is 0.9032

Step-by-step explanation:

The mean lifetime of a bulb is 580 hours.

$\mu = 580 hours$

The standard deviation of the lifetime is 20 hours

$\sigma = 20 hours$

We are supposed to find  the probability of a bulb lasting for at most 606 hours i.e. $P(X\leq 606)$

Formula :$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{606-580}{20}$

Z=1.3

Refer the z table

$P( X \leq 606)=0.9032$

Hence the probability of a bulb lasting for at most 606 hours is 0.9032