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Chapter 4: Q.27 (page 284)

On average, how many years would you expect a physics major to spend doing post-graduate research?

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.

• Let X=the number of years a student will study ballet with the teacher.

• Let P(x)=the probability that a student will study ballet x years.

Short Answer

Expert verified

A physics major can expect to spend 2.6 years doing post-graduate research on average.

Step by step solution

01

Given Information

A physics professor wants to know what percentage of physics students will undertake post-graduate research in the coming few years. He is given the following probability distribution:

02

Calculation

The total of the probability of all the values measured by a variables is 1, so the sum of the P(X) column equals one.

0.35+0.20+0.15+P(4)+0.10+0.05=1

P(4)+0.85=1

so,

P(4)=1-0.85=0.15

The estimation of theXVariables, which is produced by multiplication of xbyp(x)and then adding all values, is the average number of years that a physics major is predicted to spent pursuing post-graduate study.

03

Explanation

The expression is framed as :

1(0.35)+2(0.20)+3(0.15)+5(0.10)+6(0.05)=0.35+0.40+0.45+0.60+0.50+0.30=2.6

As a result, a physics major may estimate to spent 2.6years pursuing post-graduate study on average.

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Most popular questions from this chapter

For the given values of the random variable X, fill in the corresponding probabilities

Approximately 8%of students at a local high school participate in after-school sports all four years of high school. A group of 60seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of

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a. In words, define the random variable X.

b. List the values that Xmay take on.

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all four years of high school? Justify your answer numerically.

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d. Construct a PDF.

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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?
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