the Weight of crackers in a box is stated to be 16 oz the am

Solution

the Weight of crackers in a box is stated to be 16 oz. the amount that the packaging machine puts in the boxes is believed to have a normal model with a mean 16.15 oz. and standard deviation of 0.3 oz.

A) What is the probability that the mean weight of a 10-box case of crackers is below 16 oz?

Standard error = sd/sqrt(n) = 0.3/SQRT(10) =0.0949

Z value for 16, z=(16-16.15)/0.0949 = -1.58

P( x < 16) =P( z < -1.58)

= 0.0571

B) What is the range of the weights for the middle 95% of boxes of crackers?

Z value for middle 95% = -1.96 and 1.96

The limits are( mean ± z*sd)

Lower weight =16.15-1.96*0.3 = 15.562

upper weight =16.15+1.96*0.3 = 16.738

The required range =(15.562, 16.738)

C) What is the range of the mean weights for the middle 95% of 10-box cases of crackers?

Z value for middle 95% = -1.96 and 1.96

The limits are( mean ± z*se)

Lower weight =16.15-1.96*0.0949 = 15.964

upper weight =16.15+1.96*0.0949 = 16.336

The required range =(15.964, 16.336)