Question

The results of the test given to students are assume to be normally distributed with a mean of 57 and a standard deviation of 10. The passing score for the exam is 30.  Answer in figure only.

a) If a student is randomly selected, what is the probability that he or she passed the exam? Answer in 4 decimal places. Answer in percentage in in 2 decimal places.

b) A score of 75 or greater is needed to obtain an A on the exam. What percentage of the students received an A? Answer in 2 decimal places.

Answer 1

solution:

From the given information

The results of the test given  to  students are normally distributed with

Mean () = 57

Standard deviation () = 10

a)

Probability that a randomly selected student passed = P(X>30)

=

= P(Z>-2.7)

= P(Z<2.7)

= 0.9965 [since,using standard normal distribution table ]

  Probability that a randomly selected student passed = 0.9965 (i.e., 99.65% )

b)

Percentage of students received A = P(X>=75)

=

= P(Z>1.8)

= 1 - P(Z<=1.8)

= 1 - 0.9641

= 0.0359   [since,using standard normal distribution table ]

Percentage of students received A = 3.59%