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In: Statistics and Probability

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.6...

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.6 years, and standard deviation of 0.5 years. If 6 items are picked at random, 3% of the time their mean life will be less than how many years? Give your answer to one decimal place.

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Expert Solution

We will let the 'X' be the variable representing the lifetime of the items.

We have been asked to find an information based on the means of the items from a sample of 6 items. We will thereforereqire a distribution of the mean of the items

z-score =

3% of the mean life should be less than '' that means the cumulative probability of is 3%. Using the normal percentage tables we can get the probability. The tables provide for values with greater than values and with p < 0.5 so we need to set the eqations accordingly.

= 1.8808

  years.

orchestra answered 2 years ago
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