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Chapter 6: Q.1.2 (page 344)

North Carolina State University posts the grade distributions for its courses online.3Students in Statistics 101in a recent semester received 26%As,42%Bs,20%Cs,10%Ds, and 2%Fs. Choose a Statistics 101student at random. The student’s grade on a four-point scale (with A=4) is a discrete random variable Xwith this probability distribution:

Write the event “the student got a grade worse than C” in terms of values of the random variable X. What is the probability of this event?

Short Answer

Expert verified

The required probability is 0.138.

Step by step solution

01

Given Information

North Carolina State University posts the grade distributions for its courses online3Students in Statistics 101in a recent semester received 26%As, 42%Bs, 20%Cs, 10%Ds, and2%Fs. Choose a Statistics 101student at random. The student’s grade on a four-point scale (with ) is aC"discrete random variable Xwith this probability distribution:

02

Explanation

According to the information, the probability distribution is

Value0
1
2
3
4
Probability0.011
0.032
0.138
0.362
0.457

The student getting a grade lesser than C′′in terms of Xcould be written as X≤2.

P(X≤2)is calculated as:

localid="1649918435222" P(X≤2)=1−(0.11+0.032+0.362+0.457)=0.138

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