Question

The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours.what is the probability that a bulb picked at random from this company product will have a life time of at least 300 hours?

Answer 1

5.37% probability that a bulb picked at random from this company product will have a life time of at least 300 hours

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

`\mu = 210, \sigma = 56`

What is the probability that a bulb picked at random from this company product will have a life time of at least 300 hours?

This is 1 subtracted by the pvalue of Z when X = 300. So

`Z = (X - \mu)/(\sigma)`

`Z = (300 - 210)/(56)`

`Z = 1.61`

`Z = 1.61` has a pvalue of 0.9463

1 - 0.9463 = 0.0537

5.37% probability that a bulb picked at random from this company product will have a life time of at least 300 hours