Question

A machine that is programmed to package 1.50 pounds of cereal is being tested for its accuracy in a sample of 54 cereal boxes, the sample mean filling weight is calculated as 1.52 pounds. The population standard deviation is known to be 0.06 pounds. Find the 95% confidence interval for the population mean filling weight.

a [1.5040, 1.5360]

b [1.4221, 1.5565]

c [1.4648, 1.5798]

d [1.4451, 1.5967]

Answer 1

Solution :

Given that,

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 0.06 /   54)

= 0.0160

At 95% confidence interval estimate of the population mean is,

- E < < + E

1.52 - 0.0160

(1.5040 , 1.5360)

Correct option is a