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=70
find the probability of a sample mean being greater than
225 if mu equals 224 and sigma equals 5.9.
For a sample of n=70, the probability of a sample mean being greater than
225 if mu equals 224 and sigma equals 5.9 is
Would the given sample mean be considered unusual?
The sample mean would not would be considered unusual because it does not lie lies within the range of a usual event, namely within 1 standard deviation 2 standard deviations
3 standard deviations
of the mean of the sample means.
Given that, mean = 224
standard deviation = 5.9
sample size ( n ) = 70
We want to find,
Therefore,
the probability of a sample mean being greater than
225 if mu equals 224 and sigma equals 5.9 is 0.0778
Here, z = 1.42 is lies within z = -2 to z = 2
The sample mean would not be considered unusual because it lies within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
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