Alarge manufacturing firm tests job applicants who recently graduated from college. the test scores are normally distributed with a mean of 500 and a standard deviation of 50. management is considering placing a new hire in an upper level management position if the person scores in the upper 6 percent of the distribution. what is the lowest score a college graduate must earn to qualify for a responsible position?

a. 50

b. 625

c. 460

d. 578

lowest score a college graduate must earn to qualify for a responsible position is 578

correct option is D. 578

Step-by-step explanation:

given data

mean = 500

standard deviation = 50

distribution = 6 %

to find out

What is the lowest score a college graduate must earn to qualify for a responsible position

solution

we know that here Probability P that is express as

P ( Z > x ) = 100% - 6%      1

so with the help of normal table

here value of Z is =  1.55 from cumulative probability 0.94

so by z score formula here x will be

x = z × standard deviation +  mean    2

so put here value

x = 1.55 × 50 + 500

x = 577.7387 ~ 578

so lowest score a college graduate must earn to qualify for a responsible position is 578

391.6 is the correct answer