Question

Your stats instructor graded your exams (0 to 100) and provided the exam summary statistics before returning the exam papers. Exams scores were normally distributed with a mean of 70.5 and a standard deviation of 12.5. He assigns letter grades based on 100 points: 90 or higher is A; 80 < 90 is B; 70 < 80 is C; 60 < 70 is D; a

Answer 1

Answer:

The probability that a randomly selected student received a C or higher is 0.5160.

Step-by-step explanation:

Let X = scores received in an exam.

The random variable X follows a Normal distribution with parameters μ = 70.5 and σ = 12.5.

The stats instructor also graded the exams.

The grades were allotted as follows:

Scores    Grades

 > 90            A

90 - <80       B

80 - <70       C

70 - <60       D

  60 <           F

Compute the probability that a randomly selected student received a C or higher as follows:

P (C or higher) = P (X > 70)

                        $=P(\frac{X-\mu}{\sigma}>\frac{70-70.5}{12.5})\\=P(Z>-0.04)\\=P(Z<0.04)\\=0.5160$

*Use a z-table for the probability.

Thus, the probability that a randomly selected student received a C or higher is 0.5160.