Question

Question 7465: The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000970 mm. Assume a random sample of 48 sheets of metal resulted in an x¯ = .1646 mm. Calculate the 95 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) The 95% confidence interval is from ___ to ___

a) .1606, .1686

b) .1622, .1670

c) .1636, .1656

d) .1642, .1650

Answer 1

We are 95% confident that the true mean metal thickness is between 0.1627 mm and 0.1665 mm. None of the given options is answer.

Step-by-step explanation:

A confidence interval is a range of values that is likely to contain the true population mean. The width of the confidence interval depends on the sample size, the standard deviation, and the level of confidence. In this case, the sample size is 48, the standard deviation is 0.000970 mm, and the level of confidence is 95%.

We can use the formula below to calculate the confidence interval:

xbar ± z*σ/√n

where:

x bar is the sample mean

z* is the z-score for the desired level of confidence

σ is the population standard deviation

n is the sample size

Plugging in the values, we get:

0.1646 ± 1.96*(0.000970)/√48

0.1646 ± 0.0019

Therefore, we are 95% confident that the true mean metal thickness is between 0.1627 mm and 0.1665 mm.

None of the given options is answer.