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Chapter 6: Q.1.3 (page 344)

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’s 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 .

Short Answer

Expert verified

All the tail of the bar is to the left. Thus, the distribution is skewed to the left

Step by step solution

01

Given information

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 Statistics101student at random. The student’s grade on a four-point scale (with A = 4) is a discrete random variable Xwith this probability distribution:

02

Given information

From Question(1.2) The probability distribution is

The following is an example of a probability distribution:

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Most popular questions from this chapter

Keno is a favorite game in casinos, and similar games are popular in the states that operate lotteries. Balls numbered 1to 80are tumbled in a machine as the bets are placed, then 20of the balls are chosen at random. Players select numbers by marking a card. The simplest of the many wagers available is “Mark 1Number.” Your payoff is 3on a bet if the number you select is one of those chosen. Because 20of 80numbers are chosen, your probability of winning is 20/80, or 0.25. Let X=the amount you gain on a single play of the game.

(a) Make a table that shows the probability distribution of X.

(b) Compute the expected value of X. Explain what this result means for the player

To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class.

Let X=the number of Patti's correct guesses.

To get a passing score on the quiz, a student must guess correctly at least 6times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.

Rotter Partners is planning a major investment. The amount of profit X(in millions of dollars) is uncertain, but an estimate gives the following probability distribution:

Based on this estimate, μX=3and σX=2.52

Rotter Partners owes its lender a fee of $200,000plus 10%of the profits X. So the firm actually retains Y=0.9X-0.2from the investment. Find the mean and standard deviation of the amount Ythat the firm actually retains from the investment.

Suppose you roll a pair of fair, six-sided dice until you get doubles. Let T = the number of rolls it takes. Show that T is a geometric random variable (check the BITS)

To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple choice quiz. The catch is, students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key, so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let X=the number of Patti's correct guesses.

Find P(X=3). Explain what this result means.
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