Question

A new LED light to replace incandescent bulbs has come on the market. The box says it has an average life of 8,000 hours with a standard deviation of 200 hours.

- What is the probability that a single bulb will last between 7950 and 8100 hours?

- What is the probability that the mean of a sample of 75 bulbs picked at random will be between 7950 and 8100 hours?

Answer 1

Solution :

Given that,

mean = $\mu$ = 8000

standard deviation = $\sigma$ = 200

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 200/ $\sqrt$ 75 = 23.0940

= P[(7950 - 8000) /23.0940 < ($\bar x$ - $\mu$ _{$\bar x$}) / $\sigma$ _{$\bar x$} < (8100 - 8000) /23.0940 )]

= P(-2.17 < Z < 4.33)

= P(Z < 4.33) - P(Z < -2.17)

= 1 - 0.0150

= 0.985

Probability = 0.985