A set of data is normally distributed with a mean of 37 and a standard deviation...

A set of data is normally distributed with a mean of 37 and a standard deviation of 1.5. If you randomly select a data point and it is 37.75, which of the following would describe that data point?

Unusually large (Statistically significant)
Unusually small (Statistically significant)
Not unusual (Not statistically significant)
Not enough information

Solutions

Expert Solution

Solution:

We are given that: a set of data is normally distributed with a mean of 37 and a standard deviation of 1.5.

That is: Mean = and standard deviation =

A data point is randomly selected and it is 37.75

That is: x = 37.75

We have to describe this data point

Note that: a number is unusually high or unusually low if it is more than 2 standard deviation from the mean and we can say a number is statistically significant.

If it is less than 2 standard deviation from the mean value, then we say this number is not unusual and it is not statistically significant.

z score gives number of standard deviations from the mean value for any x value.

Thus we use z score formula to find number of standard deviations.

Thus x = 37.75 is 0.5 standard deviation from the mean value and it is within +/- 2 standard deviation from mean value.

Thus correct description of the data point is:

Not unusual (Not statistically significant)

orchestra answered 10 months ago

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