Question

In a given university, number of credits completed by a BS graduate is a normal distribution. The average credits was 128.8, with a standard deviation of 3.2.

1. A.What is the chance that a randomly selected BS degree graduate completed over 133 credits?
2. What proportion of graduates will finish between 125 and 134 credits?
3. Among graduates, what is the lowest number of credits which is among top 1.5% of students with earned credits?
4. Kelly is graduating this semester, a student once heard that she took lots of classes unnecessary for the degree (could be due to the fact that she likes to learn), so it is reasonable to assume that she earned over 133 credits, what is the chance that she studied over 138 credits?
5. If we randomly select 10 graduates, what is the chance that 4 of them earn less than 138 credits?

Answer 1

X denotes number of credits completed by a BS graduate

• P(X>133)=0.09467574

• P(125<X<134)=0.8304035

  proportion of graduates will finish between 125 and 134 credits=0.83(Approximate).

• We are to find 'x' credits such that P(X>x)=.015.

Here x=135.7443

• P(X>138|X>133)=P(X>138)/P(X>133)=0.02133743.

Y denotes number of students earned less than 138 credits.

P(Y=4)=1.33328e-14