What fraction of sample means from samples of size n = 40 fall within ±3 gizmos from the population mean?

What fraction of sample means from samples of size n = 40 fall within ±3 gizmos from the population mean?

Question 1 and 2 are related
You run a gizmo factory. Over the past year the average output of the factory is 480 gizmos and the standard deviation of that output is 10 units per day.

1 What fraction of sample means from samples of size n = 40 fall within ±3 gizmos from the population mean?

a 0.8714
b 0.8990
c 0.9426
d 0.9728

2 Using the population mean and standard deviation above, in repeated samples of size n = 40, 95% of sample means fall within that fall within ±_____ gizmos from the population means.

a 3.9
b 3.5
c 3.1
d 2.7


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