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Chapter 7: Problem 1

State whether each of the following random variables is discrete or continuous: a. The number of defective tires on a car b. The body temperature of a hospital patient c. The number of pages in a book d. The number of draws (with replacement) from a deck of cards until a heart is selected e. The lifetime of a lightbulb

Short Answer

Expert verified
a. Discrete; b. Continuous; c. Discrete; d. Discrete; e. Continuous.

Step by step solution

01

Distinguish Between Discrete and Continuous Variables

This involves identifying whether the random variable under consideration can take on any value within a given interval (continuous) or can only take on distinct, separate values (discrete).
02

Apply Identification to Each Variable

Identify each variable as either discrete or continuous based on the parameter it measures: a. The number of defective tires on a car - This is a discrete variable because the number of defective tires can only be an integer. b. The body temperature of a hospital patient - This is a continuous variable because body temperature can take any value in a certain range. c. The number of pages in a book - This is a discrete variable because the number of pages in a book must be a whole number. d. The number of draws (with replacement) from a deck of cards until a heart is selected - This is a discrete variable because the number of draws is countable. e. The lifetime of a lightbulb - This is a continuous variable because the life of a product can take any value in a certain range.

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Most popular questions from this chapter

Suppose that in a certain metropolitan area, nine out of 10 households have cable TV. Let \(x\) denote the number among four randomly selected households that have cable TV, so \(x\) is a binomial random variable with \(n=4\) and \(p=.9\). a. Calculate \(p(2)=P(x=2)\), and interpret this probability. b. Calculate \(p(4)\), the probability that all four selected households have cable TV. c. Determine \(P(x \leq 3)\).

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Flashlight bulbs manufactured by a certain company are sometimes defective. a. If \(5 \%\) of all such bulbs are defective, could the techniques of this section be used to approximate the probability that at least five of the bulbs in a random sample of size 50 are defective? If so, calculate this probability; if not, explain why not. b. Reconsider the question posed in Part (a) for the probability that at least 20 bulbs in a random sample of size 500 are defective.

Suppose that for a given computer salesperson, the probability distribution of \(x=\) the number of systems sold in 1 month is given by the following table: \(\begin{array}{lllllllll}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\end{array}\) \(\begin{array}{lllllllll}p(x) & .05 & .10 & .12 & .30 & .30 & .11 & .01 & .01\end{array}\) a. Find the mean value of \(x\) (the mean number of systems sold). b. Find the variance and standard deviation of \(x\). How would you interpret these values? c. What is the probability that the number of systems sold is within 1 standard deviation of its mean value? d. What is the probability that the number of systems sold is more than 2 standard deviations from the mean? $\begin{array}{llll}
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