Question

1. Plastic bags used for packaging produce are manufactured so that the breaking strengths of the bags are normally distributed with a standard deviation of 1.8 pounds per square inch. A random sample of 16 bags is selected. The probability is .15 that the sample mean exceeds the population mean by more than or equal to how much? 2. Plastic bags used for packaging produce are manufactured so that the breaking strengths of the bags are normally distributed with a standard deviation of 1.8 pounds per square inch. What proportion of bags will exceed the average breaking strength by more than 3 pounds?

Answer 1

1. z score corresponding to top 15% area = 1.036

Hence,

Required Difference = 1.036*1.8/$\sqrt{16}$ = 0.4662

2. z score = 3/1.8 = 1.67

Hence,

Required proportion = P(z > 1.67) = 0.0478