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Chapter 6: Q.1.1 (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 X with this probability distribution:

Say in words what the meaning ofP(X≥3) is. What is this probability?

Short Answer

Expert verified

P(X≥3)represents the probability that student will get a Bor more.

The required probability is 0.819.

Step by step solution

01

Given information 

Given in the question that, the North Carolina State University posts the grade distributions for its courses online.3 Students in Statistics 101 in 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 A = 4) is a discrete random variable Xwith this probability distribution:

02

Explanation

The table is:

Value
0
1
2
3
4
Probability
0.011
0.032
?.362
0.457

To explain the term, the missing value is required to be computed. Let the missing value be x. The missing value can be calculated as:

localid="1649851625209" 0.011+0.032+x+0.362+0.457=1

x+0.862=1

x=0.138

P(X≥3)can be calculated as:

localid="1649918332279" P(X≥3)=P(X=3)+P(X=4)=0.362+0.457=0.819

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Most popular questions from this chapter

83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don’t reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define D=X-Y.

Compute σDassuming that XandY are independent. Show your work

Compute and interpret the standard deviation ofX.

Spell-checking Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X. Show your work

A large auto dealership keeps track of sales made during each hour of the day. Let X=the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of Xis as follows:

Compute and interpret the mean of X.
See all solutions

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