Question

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. Between what two values symmetrically distributed around the mean will 95% of the breaking strengths fall?

Answer 1

= 5, =1.5

we want to find such value that 95% of the breaking strengths fall between those two values

to get this we use z-score

Now using normal z table find z score for 0.95

we get

Z-Score for 95% is ( Z ) = 1.96

thus 95% fall between

- (z * ) and + (z * )

5 - ( 1.96 * 1.5) and  5 + ( 1.96 * 1.5)

2.06 and 7.94

95% of the breaking strengths fall between 2.06 and 7.94