The population mean and standard deviation are given below F

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n=66, find the probability of a sample mean being less than 24.2. If mu=24 and sigma =1.24. Would the given sample mean be considered unusual? The sample mean would be considered unusual because it has a probability that is greater than 5%.

Solution

A)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    24.2      
u = mean =    24      
n = sample size =    66      
s = standard deviation =    1.24      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.31      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.31   ) =    0.9049 [ANSWER]

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The sample mean WOULD NOT be considered unusual because it has a probability taht is GREATER than 5%. [ANSWER]

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Note that unusual events have probability of less than 5%.