The average repair cost of a microwave oven is 55 with a sta

The average repair cost of a microwave oven is $55 with a standard deviation of $8. The cost are normally distributed. If 12 ovens are repaired, find the probability of the mean of the repair bills will be between $50 and $61.

Solution

P( 50< x < 61)

P( [50-55] / [8 / srqt(12)] < z < [61-55]/ [8 / srqt(12)]

P( 2.17<z< 2.60) = P( z > 2.17) - P8 z > 2.60)

using tables of normal distribution

P( 2.17<z< 2.60) = 0.0150 - 0.00466 = 0.01034