A distribution of values is normal with a mean of 114.5 and a standard deviation of 23. Find P47, which is the score separating the bottom 47% from the top 53%.
P47 =
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.

The score separating the bottom 47% from the top 53% is 112.8

Step-by-step explanation:

Let X denote the random variable whose values are normal with a mean of 114.5 and a standard deviation of 23.

Compute the 47th percentile as follows:

The corresponding z-value is,

z = -0.075

*Use the z-table.

Compute the value of x as follows:

Thus, the score separating the bottom 47% from the top 53% is 112.8

step-by-step explanation: