A distribution of values is normal with a mean of 116.7 and a standard deviation of 73.3

Question

Find P₆₈, which is the score separating the bottom 68% from the top 32%.

Find P_{68=_______________________}

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

The z-score for 68% or .68 is 0.468

Z = 0.468 in the table. So using the formula: Z = (x - 𝝁)/σ

Where:

Z = Z score

x = is the raw score

𝝁 = mean

σ = standard deviation

0.468 = (x - 116.7) / 73.3

x = 166.5 = P₆₈