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Suppose the scores of a new standardized math test are Normally distributed with an unknown mean and an unknown standard deviation. A simple random sample of

`n=25`

students yields an average score of

`\bar{x} =525`

and a standard deviation of

`s=60`

. (a) Construct and interpret a

`90%`

confidence interval for the population mean. (b) Construct and interpret a

`95%`

confidence interval for the population mean. (c) What sample size would be needed to make the margin of error for the

`90%`

confidence no more than 7 . (d) What sample size would be needed to make the margin of error for the

`95%`

confidence no more than 7 .