The Exponential Distribution Quiz
The question sheet
Reveal any answer as you study-
The exponential distribution is often concerned with what?
- The number of successes in trials
- The amount of time until an event occurs
- The categories of nominal data
- The correlation between two variables
Reveal answer
Answer: The amount of time until an event occurs
Source evidence
PDF page 334: The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the length, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. It can be shown, too, that the value of the change that you have in your pocket or purse approximately follows an exponential distribution. Values for an exponential random variable occur in the following way. There are fewer large values and more small values. For example, the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are more people who spend small amounts of money and fewer people who spend large amounts of money. Exponential distributions are commonly used in calculations of product reliability, or the length of time a product lasts.
-
For an exponential random variable, values occur in what pattern?
- Equal numbers of all values
- More large values, fewer small values
- Only values above the mean
- Fewer large values, more small values
Reveal answer
Answer: Fewer large values, more small values
Source evidence
PDF page 334: The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the length, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. It can be shown, too, that the value of the change that you have in your pocket or purse approximately follows an exponential distribution. Values for an exponential random variable occur in the following way. There are fewer large values and more small values. For example, the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are more people who spend small amounts of money and fewer people who spend large amounts of money. Exponential distributions are commonly used in calculations of product reliability, or the length of time a product lasts.
-
For a postal clerk with mean time of four minutes, what is the decay parameter m?
- 2.8
- 0.25
- 0.5
- 4
Reveal answer
Answer: 0.25
Source evidence
PDF page 334: Let X = amount of time (in minutes) a postal clerk spends with his or her customer. The time is known to have an exponential distribution with the average amount of time equal to four minutes. X is a continuous random variable since time is measured. It is given that μ = 4 minutes. To do any calculations, you must know m, the decay parameter. 1 1
PDF page 334: m = . Therefore, m = = 0.25.
-
In the exponential distribution, the standard deviation σ is:
- Half the mean
- The square of the mean
- The same as the mean
- Zero
Reveal answer
Answer: The same as the mean
Source evidence
PDF page 334: The standard deviation, σ, is the same as the mean. μ = σ
-
The distribution notation for the exponential distribution is:
- X ~ Exp(m)
- X ~ B(n, p)
- X ~ U(a, b)
- X ~ N(μ, σ)
Reveal answer
Answer: X ~ Exp(m)
Source evidence
PDF page 334: The distribution notation is X ~ Exp(m). Therefore, X ~ Exp(0.25).
-
In the exponential probability density function, the number e is approximately:
- 3.14159
- 2.71828
- 0.25000
- 1.41421
Reveal answer
Answer: 2.71828
Source evidence
PDF page 334: The probability density function is f(x) = me . The number e = 2.71828182846... It is a number that is used
-
On the exponential graph, the maximum value on the y-axis equals:
- μ
- σ
- m
- 0
Reveal answer
Answer: m
Source evidence
PDF page 335: = (0.25)(1) = 0.25 = m. The maximum value on the y-axis is m.
-
The exponential distribution graph is described as:
- A horizontal line
- A bell-shaped curve
- A rectangle
- A declining curve
Reveal answer
Answer: A declining curve
Source evidence
PDF page 335: Notice the graph is a declining curve. When x = 0,
-
For the postal clerk, the probability that a clerk spends four to five minutes is:
- 0.6321
- 0.7135
- 0.0814
- 0.072
Reveal answer
Answer: 0.0814
Source evidence
PDF page 336: The probability that a postal clerk spends four to five minutes with a randomly selected customer is P(4 < x < 5)
PDF page 336: = P(x < 5) – P(x < 4) = 0.7135 − 0.6321 = 0.0814.
-
For the postal clerk, half of all customers are finished within how long?
- 4 minutes
- 5 minutes
- 0.25 minutes
- 2.8 minutes
Reveal answer
Answer: 2.8 minutes
Source evidence
PDF page 336: P(x < k) = 0.50, k = 2.8 minutes (calculator or computer)
PDF page 336: Half of all customers are finished within 2.8 minutes. You can also do the calculation as follows:
-
For a computer part lasting on average ten years, the decay parameter m is:
- 0.25
- 10
- 1
- 0.1
Reveal answer
Answer: 0.1
Source evidence
PDF page 338: μ = 10 so m = = = 0.1
-
The probability that a computer part lasts more than seven years is:
- 0.4966
- 0.0737
- 0.5934
- 0.6671
Reveal answer
Answer: 0.4966
Source evidence
PDF page 338: P(x > 7) = e = 0.4966. The probability that a computer part lasts more than seven years is 0.4966.
Introductory Statistics
Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
Make your own — free
Turn any notes into a game in under a minute. Free to start.