Chapter 7, Problem 20P

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Chapter
Section

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages μ. = 12.5 with a standard deviation of s = 1, and forms a normal distribution. What is the probability of randomly picking a sample of n = 25 1-pound bags that average more than M = 13 shrimp per bag?

To determine
The probability of obtaining a sample of n=251-pound bags that average more than 13 shrimp per bag.

Explanation

Given info:

The number of jumbo shrimp in a 1-pound bag average is μ=12.5 with the standard deviation s=1 and it follows a normal distribution. The sample size is n=25 and the sample mean is M=13 .

Calculation:

The distribution of sample means is normal with the parameters μx¯ and σx¯, by using the central limit theorem.

The mean of the sampling distribution of sample means is given below:

μM=μ

Here, the population mean is μ=12.5. Therefore, the sampling distribution of the sample mean is μM=12.5.

The formula to find the standard deviation of the sample means (σM) is as follows:

σM=σn

Substitute 1 for σ and 25 for n

σM=125=15=0.2

Thus, the standard deviation of the sampling distribution of sample means is σM=0

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