Question

For the following question, answer A, B, and C. A competency test for students has a normal distribution with a mean of 400 and a popularion standard deviation of 100.

A. Find the probability that a randomly selected student has a score between 250 and 550.

B. Find the probablity that a randomly selected student has a score greater than 550. C. The top 3% of students receive $500. What is the minimum score you would need to receive this award?

Answer 1

As it is normal distribution we can convert x into z

A.Find the probability that a randomly selected student has a score between 250 and 550

We need to find P(250<x<550)=

So P(250<x<550)=0.8664

B. Find the probablity that a randomly selected student has a score greater than 550

Here we need to find P(x>550)=

So P(x>550)=0.0668

C.The top 3% of students receive $500. What is the minimum score you would need to receive this award?

Here we need to find x such that P(x>0.03).according to z tabelP(x>0.03)=1.881

x=(1.881*100)+400=188.1+400=588.1

So x=588.1