In a random sample of 35 boxes of cereal, the mean volume was 24.03 ounces. The...

In a random sample of 35 boxes of cereal, the mean volume was 24.03 ounces. The population standard deviation of the volume is known to be 0.005 ounces. Explain which distribution and which formula(s) you would use to construct a confidence interval for the population mean.

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Expert Solution

the sample size given for the cereal boxes = 35

the population standard deviation = 0.005

since population standard deviation is known and sample size is also greater than 30 then according to the Central limit theorem the sampling distribution is approximately the normal distribution with

and standard deviation = .

when populatin standard deviatin is known we will use the z-distribution to find out the confidence interval

so margin of error will be :

the value of z is obtained by the normal distribution table on some given significance level.

and confidence interval is given by

orchestra answered 1 year ago

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