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?
deviation is 8. About what percent of the observations lie between 84 and 116?
Answers
MathGuru
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.
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.
sara
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
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