91Ó°ÊÓ

Identify the mistake in the probability distribution table.

Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics

majors will spend the next several years doing post-graduate research. He has the following probability distribution.

Define the random variable X.

Define $P(x),$or the probability of$x.$

Find the probability that a physics major will do post-graduate research for four years.

$P(x=4)=\_\_\_\_\_\_\_$

Find the probability that a physics major will do post-graduate research for at most three years. $P(x≤3)$ = _______

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 $P\left(x\right)=$the probability that a student will study ballet x years.

Complete Table 4.28 using the data provided.

In words, define the random variable X.

$P(xâ‰\yen 5)$

$P(x=4)=\_\_\_\_\_\_\_$P(x = 4) = _______