Question

The thickness of lenses used in eyeglasses are known to be Normally distributed with a population standard deviation (?) of 0.5 mm. A sample of 50 lenses gives a sample mean thickness of 3.05 mm.

a.) Create a 95% confidence interval for the true average thickness of the lenses.

b.) The manufacturer of the lenses claims that the true average thickness of the lenses is 3.20 mm. Based on your confidence interval calculation above, is this claim believable? Briefly explain why or why not.

Answer 1

given data are:-

sampel size (n) = 50

sampel mean () = 3.05

population sd () = 0.5

a).z critical value for 95% confidence level, both tailed test be:-

the 95% confidence interval for the true average thickness of the lenses is:-

b).The manufacturer of the lenses claims that the true average thickness of the lenses is 3.20 mm.

Based on the confidence interval calculation above, this claim is not believable because the value 3.20 is outside of the confidence interval.

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