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Chapter 6: Problem 7

State whether each of the following random variables is discrete or continuous. a. The number of courses a student is enrolled in b. The time spent completing a homework assignment c. The length of a person's forearm d. The number of times out of 10 throws that a dog catches a Frisbee

Short Answer

Expert verified
a. Discrete \n b. Continuous \n c. Continuous \n d. Discrete

Step by step solution

01

- Analyzing Variable a.

The first variable is the number of courses a student is enrolled in. You can count the number of courses, and there can't be a fraction of a course. Therefore, this variable is discrete.
02

- Analyzing Variable b.

The second variable is the time spent completing a homework assignment. Time is a continuous measure, it can take any positive value, and it can also be broken down into smaller units indefinitely (seconds can be broken down into milliseconds, etc.). Therefore, this variable is continuous.
03

- Analyzing Variable c.

The third variable is the length of a person's forearm. Similar to time, length is a continuous measure, it can take any positive value, and it can also be broken down into smaller units indefinitely. Therefore, this variable is continuous.
04

- Analyzing Variable d.

The final variable is the number of times out of 10 throws that a dog catches a Frisbee. This variable is countable and can't take a fraction, therefore, this variable is discrete.

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Most popular questions from this chapter

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.

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 \(\mathrm{E}\) ?

An appliance dealer sells three different models of freezers having \(13.5,15.9,\) and 19.1 cubic feet of storage space. Let \(x=\) the amount of storage space purchased by the next customer to buy a freezer. Suppose that \(x\) has the following probability distribution: $$ \begin{array}{lrrr} x & 13.5 & 15.9 & 19.1 \\ p(x) & 0.2 & 0.5 & 0.3 \end{array} $$ a. Calculate the mean and standard deviation of \(x\). (Hint: See Example 6.15\()\) b. Give an interpretation of the mean and standard deviation of \(x\) in the context of observing the outcomes of many purchases.

According to the paper "Commuters' Exposure to Particulate Matter and Carbon Monoxide in Hanoi, Vietnam" (Transportation Research [2008]: 206-211), the carbon monoxide exposure of someone riding a motorbike for \(5 \mathrm{~km}\) on a highway in Hanoi is approximately normally distributed with a mean of 18.6 ppm. Suppose that the standard deviation of carbon monoxide exposure is 5.7 ppm. Approximately what proportion of those who ride a motorbike for \(5 \mathrm{~km}\) on a Hanoi highway will experience a carbon monoxide exposure of more than 20 ppm? More than \(25 \mathrm{ppm} ?\)

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?
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