The answer is the option d, which is: d) 
The explanation for this problem is shown below:
1. Smplify the denominator and rewrite the numerator in this form:

2. Multiply the denominator and the numerator by the conjugated
and simplify the expression, as following:

3. As you can see, you obtain the expression shown in the option mentioned above.
About 3.4% large according to the coordinates
Answer:
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
7 + 5 + 4 = 16, so probability of getting a red is 4 out of 16 which can be simplified as 1 in 4 chances