Question

A company produces large fans to circulate air in warehouses. The working lifetime of each fan produced is distributed normally with a mean of 72 months and a standard deviation of 8 months

Answer 1

The probability that a randomly selected fan produced by the company has a lifetime of above X=60 months is 0.9332 or 93.32%.

What is the normally distributed data?

Normally distributed data is the distribution of probability which is symmetric about the mean. The mean of the data is the average value of the given data.

The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

A company produces large fans to circulate air in warehouses.

The working lifetime of each fan produced is distributed normally, with a mean of 72 months and a standard deviation of 8 months. Thus,

$\mu=72\\\sigma=8$

The z score can be find out as,

$Z=\dfrac{X-\mu}{\sigma}$

The probability that a randomly selected fan has lifetime of above X=60 months is,

$Z=\dfrac{60-72}{8}\\Z=-1.5$

Here, P(Z>-1.5)=1-P(Z-1.5). For this p value in the z table, we get the probability as,

$P=1-0.0668\\P=0.9332\\P=93.32\%$

Thus, the probability that a randomly selected fan produced by the company has a lifetime of above X=60 months is 0.9332 or 93.32%.

Learn more about the normally distributed data here;

brainly.com/question/6587992

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