Question

In: Statistics and Probability

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.2...

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.2 years, and standard deviation of 3 years.

If 5 items are picked at random, 7% of the time their mean life will be less than how many years?

Give your answer to one decimal place.

Solutions

Expert Solution

Given that,

mean = = 9.2 years.

standard deviation = = 3 years.

n = 5

=   = 9.2

= / n = 3/ 5 = 1.34

Using standard normal table

P(Z < z) = 7%

P(Z < z ) = 0.07

P(Z < -1.476 ) = 0.07

z = -1.476

Using z-score formula

= z * +

= -1.476 * 1.34 + 9.2

= 7.2 years.

orchestra answered 2 years ago
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