Question

Suppose that a brand of lightbulb lasts on average 2710 hours with a standard deviation of 111hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that aparticular bulb will last from 2426 to 2861 hours?P(2426 < X < 2861) =Enter your answer as a number accurate to 4 decimal places.*Note: all z-scores must be rounded to the nearest hundredth.

Answer 1

P(2426 < X < 2861) =0.9079

Explanation:

• The average life of the bulb = 2710 hours

,

• The standard deviation = 111 hours

We want to find the probability that a particular bulb will last from 2426 to 2861 hours.

Using the z-score formula below:

`z=(X-\mu)/(\sigma)\text{ where }\begin{cases}{X=Raw\text{ Score}} \\ {\mu=Mean} \\ {\sigma=Standard\;Deviation}\end{cases}`

We standardize each of the given values:

[tex]\begin{gathered} P\left(2426From the z-score table:[tex]P(-2.56The probability that a particular bulb will last from 2426 to 2861 hours is 0.9079.