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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鈥檚 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鈮�3) is. What is this probability?

Short Answer

Expert verified

P(X鈮�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鈥檚 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鈮�3)can be calculated as:

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

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Most popular questions from this chapter

80. More lefties Refer to Exercise 72.

(a) Find the probability that exactly 3students in the sample are left-handed. Show your work.
(b) Would you be surprised if the random sample contained 4or more left-handed students? Compute P(W鈮�4) and use this result to support your
answer.

Exercises 47 and 48 refer to the following setting. Two independent random variables Xand Yhave the probability distributions, means, and standard deviations shown.

47. Sum Let the random variableT=X+Y.
(a) Find all possible values of T. Compute the probability that Ttakes each of these values. Summarize the probability distribution ofT in a table.
(b) Show that the mean of Tis equal to渭X+渭Y.
(c) Confirm that the variance of T is equal to 蟽X2+蟽Y2. Show that 蟽T鈮�蟽X+蟽Y.

Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made 80%of his field-goal attempts in the past. This season he attempts 20field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made 80%of his free-throw attempts in the past. This season he takes 150free throws. Basketball free throws are always attempted from 15feet away with no interference from other players

Compute and interpret the standard deviation ofX.

North Carolina State University posts the grade distributions for its courses online.3Students in Statistics 101in a recent semester received 26%A42%Bs,20%Cs,10%Ds,and2%Fs. Choose a Statistics 101student at random. The student鈥檚 grade on a four-point scale (with A=4) is a discrete random variable Xwith this probability distribution:

Sketch a graph of the probability distribution. Describe what you see .
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