Question

In: Statistics and Probability

The results of the test given to students are assume to be normally distributed with a...

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.

Solutions

Expert Solution

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%


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