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# FOR A POPULATION WITH A STANDARD DEVIATION OF Σ = 20, HOW

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Author: Christine Farr
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http://theperfecthomework.com/for-a-population-with-a-standard-deviation-of-20-how-large-a-sample-is-necessary-to-have-a-standard-error-that-is/

1. For a population with a standard deviation of σ = 20, how large a sample is necessary tohave a standard error that is:a. less than or equal to 10 point?b. less than or equal to 4 points?c. less than or equal to 2 point?2. The following samples were obtained from a population with a mean of μ = 40 and a standard deviation of σ = 8. Find the z-score corresponding to each sample mean.a. A sample of n = 4 scores with M = 38b. A sample of n = 16 scores with M = 38c. A sample of n = 64 scores with M = 383. 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 on n=25 1-pound bags that average more than M=13 shrimp per bag?4. A population forms a normal distribution with a mean of μ = 75 and a standard deviation of σ = 20.a. What proportion of the sample means for n = 25 have values less than 80? In other words, find p(M < 80) for n = 25.b. What proportion of the sample means for n = 100 have values greater than 79? In other words, find p(M > 79) for n = 100.

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