The life span of a graphing calculator manufactured by Texas Instruments has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company guarantees that any calculator that starts malfunctioning within 36 months of the purchase will be replaced by a new one. You apply the normal model and discover that this is approximately 1.22% of their graphing calculators. Texas Instruments has sold 75 million graphing calculators world- wide. How many of these would you expect to malfunction within 3 months (and thus need to be replaced)? Explain.

The expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

Step-by-step explanation:

Let X represents the number of graphing calculator that starts malfunctioning within 36 months of the purchase and needs to be replaced by a new one.

It is provided that X follows a normal distribution with a mean of 54 months and a standard deviation of 8 months.

Also, using the normal model it was determined that 1.22% of graphing calculator manufactured by Texas Instruments malfunctions and needs replacement.

That is,

P (X) = 0.0122

Texas Instruments has sold 75 million graphing calculators world- wide.

Compute the expected number of graphing calculators that malfunctions within 3 months and need to be replaced as follows:

E (X) = n × P (X)

        = 75 × 10⁶ × 0.0122

        = 915000

Thus, the expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

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