Question

# A Manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from...

A Manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 10 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams.

A) Describe the sampling distribution for the sample mean

B) Calculate the standard error. Show steps.

C) For a more accurate determination of the mean weight, the quality control inspectors wish to estimate it within 0.25 grams with 99% confidence (using the t-table below). How many ravioli should they sample? Show reason for choice.

 DF Alpha 8 3.3554 9 3.2498 10 3.1693

Given that, smaple size ( n) = 10

Sample mean =15 grams

Sample standard deviation ( s ) = 1.5 grams

A) since, sample size is small and population standard deviation is unknown so the sampling distribution of the sample mean is student-t distribution.

B) standard error =

=> standard error = 0.4743

C) given that, margin of error ( E ) = 0.25 grams

A 99% confidence level has critical value with df = 10 - 1= 9 is,

We want to find, the sample size ( n ),

Required sample is, 380

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