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Chapter 6: 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 light bulb

Short Answer

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

Step by step solution

01

Identify discrete variables

A variable is classified as discrete if its possible values are countable, i.e they can be enumerated. Examples a, c, d fall into this category. The number of defective tires on a car, the number of pages in a book and the number of draws from a deck of cards until a heart is selected - all consist of countable values.
02

Identify continuous variables

Continuous random variables can take any numerical value within a certain interval or range, and often represent measurements. Examples b and e are of this type. The body temperature of a hospital patient can take any value within a certain range, and similarly, the lifetime of a light bulb is measured on a continuous scale.

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Most popular questions from this chapter

The distribution of the number of items produced by an assembly line during an 8 -hour shift can be approximated by a normal distribution with mean value 150 and standard deviation 10 . a. What is the probability that the number of items produced is at most \(120 ?\) b. What is the probability that at least 125 items are produced? c. What is the probability that between 135 and 160 (inclusive) items are produced?

Suppose that in a certain metropolitan area, \(90 \%\) of all households have cable TV. Let \(x\) denote the number among four randomly selected households that have cable TV. Then \(x\) is a binomial random variable with \(n=4\) and \(p=0.9\). 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 \(P(x \leq 3)\).

Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Let \(x\) denote the number of cars observed. What are possible \(x\) values? List five different outcomes and their associated \(x\) values. (Hint: See Example 6.2)

A machine producing vitamin \(\mathrm{E}\) capsules operates so that the actual amount of vitamin \(\mathrm{E}\) in each capsule is normally distributed with a mean of \(5 \mathrm{mg}\) and a standard deviation of \(0.05 \mathrm{mg}\). What is the probability that a randomly selected capsule contains less than \(4.9 \mathrm{mg}\) of vitamin \(\mathrm{E}\) ? At least \(5.2 \mathrm{mg}\) of vitamin \(\mathrm{E}\) ?

Suppose \(x=\) the number of courses a randomly selected student at a certain university is taking. The probability distribution of \(x\) appears in the following table: $$ \begin{array}{lccccccc} x & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ p(x) & 0.02 & 0.03 & 0.09 & 0.25 & 0.40 & 0.16 & 0.05 \end{array} $$ a. What is \(P(x=4)\) ? b. What is \(P(x \leq 4)\) ? c. What is the probability that the selected student is taking at most five courses? d. What is the probability that the selected student is taking at least five courses? More than five courses? e. Calculate \(P(3 \leq x \leq 6)\) and \(P(3 < x < 6)\). Explain in words why these two probabilities are different.
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