The population mean and standard deviation are given below Find the required pro

Question

The population mean and standard deviation are given below Find the required probability For a sample of n-65 find the probabilty of a sample mean being less than 25 1 ir-2s and =134 EE click the icon to view page 1 EEB Cick the icon to view page 2 of the standard normal table of the standard normal table For a sample of n-65the probability of a sample mean being less than 25 1 if :25 and Round to four decimal places as needed ) Would the given sample mean be considered unusual? 1346 The sample mean I be considered unusual because it has a probability that is

Explanation / Answer

Population mean = 25 and standard deviation = 1.34, n = 65

For a sample mean of 25.1, the test statistic, Z = (25.1-25)/(1.34/sqrt(65)=0.601

From a standard Z-table, p-value for Z value of 0.60 is 0.2743 > 0.05. So a sample mean upto 25.1 isn't unusual.

For a p-value of 0.05, the one-sided z-distribution corresponds to a Z-value of 1.64.

This is equivalent to a sample mean of 25 - 1.64 x (1.34/sqrt(65) = 24.72

So a sample mean less than 24.72 would be considered unusual becaue that would have a probability of less than 0.05.

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