Question

suppose ACT reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9 . A university plans to award scholarships to students who’s scores are in the top 9%. what is the minimum score required for the scholarship?

Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9 %. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary. Answer 2 Points Keypad Tables If you would like to look up the value in a table. select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. Note: Selecting a cell will return the value associated with the column and row headers for that cell Normal Table 0 to z Normal Table- to-z Normal Table- to z

Answer 1

X ~ N ( µ = 21.4 , σ = 5.9 )
P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.09 = 0.91
Looking for the probability 0.91 in standard normal table to calculate critical value Z = 1.34
Z = ( X - µ ) / σ
1.34 = ( X - 21.4 ) / 5.9
X = 29.3

P ( X > 29.3 ) = 0.09