Chapter 12.7, Problem 24SR

a.

To determine

To state if the probability distribution is valid.

Answer to Problem 24SR

The probability distribution is valid.

Explanation of Solution

Given information:

The table shows a class’s grade distribution, where $\text{A}=4.0,\text{B}=3.0,\text{C}=2.0,\text{D}=1.0\text{ and F}=0$ .

  

The probability distribution is valid, because the probability for each grade is greater than $0$ and less than $1$ and the sum of the probability is $0.25+0.35+0.30+0.05+0.05=1$ .

b.

To determine

To find the probability that a student shall pass a course.

Answer to Problem 24SR

The probability that a student shall pass the test is $0.95$ .

Explanation of Solution

Given information:

The table shows a class’s grade distribution, where $\text{A}=4.0,\text{B}=3.0,\text{C}=2.0,\text{D}=1.0\text{ and F}=0$ .

  

The probability that a student shall pass a course is:

  $0.25+0.35+0.30+0.05=0.95$

Hence, the probability that a student shall pass the test is $0.95$ .

c.

To determine

To find the probability that a student chosen at random received a grade of C or better.

Answer to Problem 24SR

The probability that a student received a grade of C or better is $0.90$ .

Explanation of Solution

Given information:

The table shows a class’s grade distribution, where $\text{A}=4.0,\text{B}=3.0,\text{C}=2.0,\text{D}=1.0\text{ and F}=0$ .

  

The probability that a student received a grade of C or better is:

  $0.25+0.35+0.30=0.90$

Hence, the probability that a student received a grade of C or better is $0.90$ .