The life span of a calculator manufactured by Texas Instruments has a normal distribution with a...

The life span of a calculator manufactured by Texas Instruments has a normal distribution with a mean of 65 months and a standard deviation of 1 year. The company guarantees that any calculator that starts malfunctioning within 38 months of the purchase will be replaced by a new one. About what percentage of calculators made by this company are expected to be replaced? (Hint: Draw a picture, shade the region, label the axes.) If the company sells 5000 calculators, how many are expected to be replaced?

Solutions

Expert Solution

Let X be the random variable that denotes the lifespan of a calculator.

Given, E(X) = 65 and V(X) = 122

X Normal (65, 122)

The percentage of calculators made by the company that are expected to be replaced is given by

Therefore, 1.22% of calculators made by this company are expected to be replaced.

If the company sells 5000 calculators, then the expected number of calculators to be replaced are

5000 * P(X < 38) = 5000 * 0.0122

= 61

Therefore, if the company sells 5000 calculators, 61 of them are expected to be replaced.

orchestra answered 11 months ago

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