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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 random variable \n b. Continuous random variable \n c. Discrete random variable \n d. Discrete random variable \n e. Continuous random variable

Step by step solution

01

Definition of Discrete and Continuous Random Variables

A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,... etc. Continuous random variable is one which takes an infinite number of possible values within an interval.
02

Categorize Number of Defective Tires on a Car

The number of defective tires on a car can only be specific, countable numbers, ranging from 0 to 4. Therefore, it's a discrete random variable.
03

Categorize Body Temperature of a Hospital Patient

The body temperature of a patient can take any value within a certain range dependent on the precision of the measurement devise, not just specific, countable numbers Therefore, it's a continuous random variable.
04

Categorize Number of Pages in a Book

The number of pages in a book can only be countable, distinct numbers. Therefore, it's a discrete random variable.
05

Categorize Number of Draws from a Deck of Cards until a Heart is Selected

The number of draws from a deck of cards until a heart is selected can only be countable, distinct numbers. Therefore, it's a discrete random variable.
06

Categorize Lifetime of a Lightbulb

The lifetime of a lightbulb can take any value within a certain range, which can be any non-negative number. Therefore, it's a continuous random variable.

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Most popular questions from this chapter

A breeder of show dogs is interested in the number of female puppies in a litter. If a birth is equally likely to result in a male or a female puppy, give the probability distribution of the variable \(x=\) number of female puppies in a litter of size 5 .

The number of vehicles leaving a turnpike at a certain exit during a particular time period has approximately a normal distribution with mean value 500 and standard deviation 75 . What is the probability that the number of cars exiting during this period is a. At least \(650 ?\) b. Strictly between 400 and 550 ? (Strictly means that the values 400 and 550 are not included.) c. Between 400 and 550 (inclusive)?

Let \(x\) denote the IQ for an individual selected at random from a certain population. The value of \(x\) must be a whole number. Suppose that the distribution of \(x\) can be approximated by a normal distribution with mean value 100 and standard deviation 15 . Approximate the following probabilities: a. \(P(x=100)\) b. \(P(x \leq 110)\) c. \(P(x<110)\) (Hint: \(x<110\) is the same as \(x \leq 109 .\) ) d. \(P(75 \leq x \leq 125)\)

Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean \(\mu=5 \mathrm{ml}\) and standard deviation \(\sigma=0.2 \mathrm{ml}\) is a reasonable model for the distribution of the variable \(x=\) amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities: a. \(P(x<5.0)\) b. \(P(x<5.4)\) c. \(P(x \leq 5.4)\) d. \(P(4.64.5)\) f. \(P(x>4.0)\)

A grocery store has an express line for customers purchasing at most five items. Let \(x\) be the number of items purchased by a randomly selected customer using this line. Give examples of two different assignments of probabilities such that the resulting distributions have the same mean but quite different standard deviations.
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