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Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution.

- LetX=the number of years a student will study ballet with the teacher.

- Let P(x)=the probability that a student will study ballet xyears.

What does the column "P(x)"sum to and why?

Short Answer

Expert verified

Sum of P(x)is 1and is to be a probability of a students will study ballet.

Step by step solution

01

Table for no of students probabilty

02

Calculation of sum

For sum of P(x):

From table,

P(x1)=0.1,P(x2)=0.05

P(x3)=0.1,P(x4)=0.15

P(x5)=0.3,localid="1649787457135" P(x6)=0.2,localid="1649787464973" P(x7)=0.1

So,

P(x)=i=17P(xi)

=0.1+0.05+0.1+0.15+0.3+0.2+0.1

=1

Sum of P(x)is probability of x.

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Most popular questions from this chapter

There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. In the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and deer are used. The board has those six objects on it, also. We will play with bets being \(1. The player places a bet on a number or object. The “house” rolls three dice. If none of the dice show the number or object that was bet, the house keeps the \)1 bet. If one of the dice shows the number or object bet (and the other two do not show it), the player gets back his or her \(1 bet, plus \)1 profit. If two of the dice show the number or object bet (and the third die does not show it), the player gets back his or her \(1 bet, plus \)2 profit. If all three dice show the number or object bet, the player gets back his or her \(1 bet, plus \)3 profit. Let X = number of matches and Y = profit per game.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. List the values that Y may take on. Then, construct one PDF table that includes both X and Y and their probabilities.

e. Calculate the average expected matches over the long run of playing this game for the player.

f. Calculate the average expected earnings over the long run of playing this game for the player

g. Determine who has the advantage, the player or the house.

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

X~_____(_____,_____)

Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.

What values does the random variable X take on?

Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given in Table 4.31.

a. In words, define the random variable X.

b. What does it mean that the values zero, one, and two are not included for x in the PDF?

Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.

Construct the probability distribution function (PDF). Stop at x = 6.

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