Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

a. For a sample of n=70​, find the probability of a sample mean being greater than 213 if μ=212 and σ=5.9 is _________

​(Round to four decimal places as​ needed.)

b.Would the given sample mean be considered​ unusual?

The sample mean would or would not be considered unusual or usual because it lies or does not lie within the range of a usual​ or unusual event, namely within 1 standard or 2 standard deviations or 3 standard deviation of the sample means.

Answer 1

Hello

(a) Normal Distribution : n = 70, = 212 and = 5.9

To find: P( > 213)

We convert this to standard normal using

Now, P(Z > 1.42) = Area on the right of 1.42

=1 - P(Z < 1.42) = 1 - 0.9222 = 0.0778 i.e. 7.78%

(b) Because it lies within 1 standard deviation of the sample mean, it will be considered usual or it would not be considered unusual.

I hope this clears your doubt.

Do give a thumbs up if you find this helpful.