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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

Define P(x),or the probability ofx.

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.

a. What is the probability distribution for X?

b. Use your calculator to find the following probabilities:

i. the probability that 25 adults in the sample prefer saving over spending

ii. the probability that at most 20 adults prefer saving

iii. the probability that more than 30 adults prefer saving

c. Using the formulas, calculate the

(i) mean and

(ii) standard deviation of X.

A manufacturer of Christmas tree light bulbs knows that 3% of its bulbs are defective. Find the probability that a string of 100 lights contains at most four defective bulbs using both the binomial and Poisson distributions.

A bridge hand is defined as 13 cards selected at random and without replacement from a deck of 52 cards. In a standard deck of cards, there are 13 cards from each suit: hearts, spades, clubs, and diamonds. What is the probability of being dealt a hand that does not contain a heart?

a. What is the group of interest?

b. How many are in the group of interest?

c. How many are in the other group?

d. Let X = _________. What values does X take on?

e. The probability question is P(_______).

f. Find the probability in question.

g. Find the (i) mean and (ii) standard deviation of X

About 32% of students participate in a community volunteer program outside of school. If 30students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school. Use the TI-83+orTI-84 calculator to find the answer.
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