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Chapter 4: Q.11 (page 282)

Construct a probability distribution table for the data.

Short Answer

Expert verified

The following is the probability distribution table for random

variable X.

Step by step solution

01

Given Information

The probability distribution table of the random variable X, when Ellen has music practice three days a week with all of the three days 85%time, two days of 4%the time, one days of the time, and no days localid="1649567623387" 3%of the time and week is selected at random.

02

Concept Used

Xas the number of days Sam has music training in a week as a random variable to highlight the problem's features.

P(X)is stated to be the probability mass function of a discrete variable Xonly when, according to the assumptions of discrete distribution.

localid="1649567035087" i.P(x)鈮�0forallX

ii.鈭�P(x)=1

03

Calculation

Therefore the probability distribution tables of the random variableX

04

Step 4: Conclusion

So, the probability distribution tables of the random variable isX

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Most popular questions from this chapter

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?

The state health board is concerned about the amount of fruit available in school lunches. Forty-eight percent of schools in the state offer fruit in their lunches every day. This implies that 52% do not. What would a "success" be in this case?

Define the random variable X.

In one of its Spring catalogs, L.L. Bean庐 advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked more than once.

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. How many pages do you expect to advertise footwear on them?

e. Is it probable that all twenty will advertise footwear on them? Why or why not?

f. What is the probability that fewer than ten will advertise footwear on them?

g. Reminder: A page may be picked more than once. We are interested in the number of pages that we must randomly survey until we find one that has footwear advertised on it. Define the random variable X and give its distribution.

h. What is the probability that you only need to survey at most three pages in order to find one that advertises footwear on it?

i. How many pages do you expect to need to survey in order to find one that advertises footwear?

Find the standard deviation.
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