Question

An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the proportion of scanners that can be expected to fail within plus or minus 6 months of the mean. (Enter your answer as a percentage without the percent sign; keep 2 decimal places)

Answer 1

The answer is "36.14%"

Explanation:

The complete question is given in the attached file please find it.

`\mu =41\\\\\sigma= 4\\\\P(42<\bar{x}<48)= p(\bar{x}<48)-p(\bar{x}<42)\\\\Z =((42-41))/(4) = (1)/(4) =0.25\\\\Z =((48-41))/(4) = (7)/(4) = 1.75\\\\`

Using z-table to find the value.

`\to P(41<\bar{x}<48) = 0.9599- 0.5987 = 0.3614* 100= 36.14\%`

This means that between 42 and 48 months, 36.14 % of scanners could be predicted will break down.