Question

A machine that is programmed to package 1.50 pounds of cereal is being tested for its accuracy in a sample of 56 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 mean.

Answer 1

The 95% confidence interval for the mean is (1.535, 1.504).

It is given that a machine produces 1.50 pounds of cereal. The sample is 56 cereal boxes. The sample mean filling weight is calculated as 1.52 pounds. The population standard deviation is known to be 0.06 pounds.

Mean = 1.50 pounds

x = 1.52 pounds

Standard deviation = SD = 0.06 pounds

n = 56

We need to find the 95% confidence interval for the mean.

So, z = 1.96

So, the confidence interval would be

$x$±$z\frac{mean}{\sqrt{n} }$

$1.52$±$1.96*\frac{0.06}{\sqrt{56} }$

= $1.52$±$1.96*0.00801$

= $(1.52 + 0.0156996),(1.52 - 0.0156996)$

= $(1.535, 1.504)$

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