Question

The mean of a normal probability distribution is 100 and the standard
deviation is 8. About what percent of the observations lie between 84 and 116?

Answer 1

Use z-scores.

Formula:
z = (x - mean)/sd

You will need to calculate two z-scores:
z = (84 - 100)/8
z = (116 - 100)/8

You will see that one z-score is 2 standard deviations below the mean, and the second z-score is 2 standard deviations above the mean. Use a z-table to determine the probability between these two z-scores, then convert to a percent.

I hope this will help get you started.

Answer 2

Thanks for the guidance. Does it make sense that I would get 1?

1. z = (x - μ) / σ
z = (84-100)/8
z = -16/8
z = -2
and
z = (116-100)/8
z = 16/8
z = 2
area = .0228+.9772
Area = 1