Question

The life of lightbulbs is distributed normally. The variance of the lifetime is 900 and the mean life time of a bulb is 580 hours. Find the probability of a bulb lasting for at most 613 hours round your answer to four decimal places

Answer 1

Given:

The life of lightbulbs is distributed normally. The variance of the lifetime is 900 and the mean life time of a bulb is 580 hours.

Required:

Find the probability of a bulb lasting for at most 613 hours

Step-by-step explanation:

The mean lifetime of a bulb = 580 hours

The variance of the lifetime is 900. So, standard deviation will be 30.

`\begin{gathered} \text{ We are supposed to find the probability of a bulb lasting for at most} \\ 613hours\text{ i.e. }P(X\leq613). \\ Formula:Z=\frac{x-\mu(mean)}{\sigma(stnadard\text{ }deviation)} \\ Z=(613-580)/(30) \\ =(33)/(30) \\ =1.1 \end{gathered}`

Now from z table

`P(X\leq613)=0.86433`

Answer:

The probability of bulb lasting for at most 613 hours is 0.86433