Professor Rogers has found that the grades on the nursing final exam are normally distributed with a mean of 64 and standard deviation of 11. a) If the passing grade is 54, what percent of the class will fail

18.165%

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ

From the Question above , we are asked to find the percent of the class that will fail if the passing grade is 54.

The percent of the class that would fail is the percent of the class that has a grade less than(<) 54

Hence,

x is the raw score = 54

μ is the population mean = 64

σ is the population standard deviation = 11

For x < 11

z = 54 - 64/11

z =-0.90909

Probability value from Z-Table:

P(x<54) = 0.18165

Converting to percentage

= 0.18165 × 100

= 18.165%

Therefore, If the passing grade is 54, the percent of the class that will fail is 18.165%