Question 1

The time it takes to travel from home to the office is normally distributed with $\mu$ = 25 minutes and  = 5 minutes.What is the probability the trip takes more than 20 minutes? 
A)  .1587
B) .3333
C)  .6667
D)  .8413

Accepted Answer

The answer of The time it takes to travel from...

Question 2

Joe's Record World has two stores and sales at each store follow a normal distribution.For store 1,  = $2,000 and $\sigma$ = $200 per day; for store 2,  = $1,900 and $\sigma$ = $300 per day.Which store is more likely to have a day's sales in excess of $2200?
A) Store 1
B) Store 2
C) Store 1 and store 2 are equally likely
D) More information is needed

Accepted Answer

The answer of  Joe's Record World has two stores...

Question 3

The area of the continuous uniform probability distribution is​
A) ​triangular.
B) ​rectangular.
C) ​bell-shaped.
D) ​a series of vertical lines.

Accepted Answer

The continuous uniform probability distribution has a constant probability density function over a specified interval, resulting in a rectangular shape. The probability density function integrates to 1 over the interval, representing the total area under the curve.

Question 4

There is a lower limit but no upper limit for a random variable that follows the
A) ​uniform probability distribution.
B) ​normal probability distribution.
C) ​exponential probability distribution.
D) ​binomial probability distribution.

Accepted Answer

The exponential probability distribution is defined for non-negative values, meaning it has a lower limit of zero, but it can extend to infinity, thus having no upper limit.

Question 5

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes.What is the probability the trip takes more than 40 minutes?​
A) ​.0013
B) ​.0130
C) ​.9987
D) ​.9990

Accepted Answer

To find the probability that the trip takes more than 40 minutes, we calculate the Z-score for 40 minutes using the formula Z = (X - μ) / σ, where X is 40, μ is 25, and σ is 5. This gives us Z = (40 - 25) / 5 = 15 / 5 = 3. A Z-score of 3 corresponds to a probability of 0.9987 that a value is less than 40 minutes, so the probability of more than 40 minutes is 1 - 0.9987 = 0.0013.

Question 6

Which of the following probability distributions have the same value for mean, median, and mode​?
A) Uniform
B) Normal
C) ​Exponential
D) ​Poisson

Accepted Answer

The normal distribution is the only distribution that is symmetric and has a single peak, meaning the mean, median, and mode all have the same value. The uniform distribution has a constant probability density for all values in the range, and therefore does not have a single mode. The exponential distribution and Poisson distribution both have a single mode, but it is not necessarily equal to the mean or median.

Question 7

Which of the following are continuous random variables?
I.The weight of an elephant
II. The time to answer a questionnaire
III.The number of floors in a skyscraper
IV.The square feet of countertop in a kitchen
A)I and II only
B) III and IV only
C) I, II and IV only
D) I, II, II, and IV

Accepted Answer

I) The weight of an elephant can take on any value within a certain range, and is therefore a continuous random variable.
II) The time to answer a questionnaire is also a continuous random variable, as it can take on any value within a certain range.
III) The number of floors in a skyscraper is a discrete random variable, as it can only take on certain integer values.
IV) The square feet of countertop in a kitchen is a continuous random variable, as it can take on any value within a certain range.

Question 8

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow
A) ​a Poisson probability distribution.
B) ​a normal probability distribution.
C) ​a uniform probability distribution.
D) ​an exponential probability distribution.

Accepted Answer

The time between successive arrivals following a Poisson distribution should follow an exponential probability distribution. This is because the Poisson process assumes that the arrivals occur randomly and independently, so the time between successive arrivals should be independent and follow an exponential distribution.

Question 9

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is speed, measured in miles per hour.This random variable is a
A) ​nominal random variable.
B) ​ordinal random variable.
C) ​discrete random variable.
D) ​continuous random variable.

Accepted Answer

Speed is a continuously varying quantity and can take on any value within a certain range. Therefore, it is a continuous random variable. Options A and B are not relevant in this case because they refer to qualitative variables, and option C is not applicable because speed can take on any value within a certain range.

Question 10

The uniform distribution defined over the interval from 25 to 40 has the probability density function?
A)  f(x) = 1/40 for all x
B)  f(x) = 5/8 for 25$\text{\textless}$x $\text{\textless}$ 40 and f(x) = 0 elsewhere
C)  f(x) = 1/25 for 0 < x < 25 and f(x) = 1/40 for 26 $\text{\textless}$x $\text{\textless}$ 40
D)  f(x) = 1/15 for 25 < x $\text{\textless}$ 40 and f(x) = 0 elsewhere

Accepted Answer

The probability density function (PDF) of a uniform distribution defined over an interval [a, b] is given by f(x) = 1/(b-a) for a ≤ x ≤ b. For the interval from 25 to 40, the length of the interval is 40 - 25 = 15, so the PDF is 1/15 for 25 ≤ x ≤ 40.

Question 11

​Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is
A) ​Uniformly distributed.
B) Normally distributed.
C) ​Poisson distributed.
D) ​Exponentially distributed.

Accepted Answer

When the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is said to have a uniform distribution.

Question 12

The probability distribution that can be described by just one parameter is the​
A) ​uniform.
B) ​normal.
C) ​exponential.
D) ​binomial.

Accepted Answer

The exponential distribution can be described by just one parameter, which is the rate parameter. The other distributions listed require at least two parameters to fully describe their probability distributions.

Question 13

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes.What is the probability the trip takes between 20 and 30 minutes?​
A) ​.3413
B) ​.4206
C) ​.6826
D) ​.8413

Accepted Answer

We need to find the probability of traveling between 20 and 30 minutes, which can be written as P(20<X<30), where X is the time taken to travel.

We can standardize the distribution using the formula z = (X-μ)/σ, where μ = 25 and σ = 5:

P(20<X<30) = P((20-25)/5 < z < (30-25)/5)

= P(-1 < z < 1)

From the standard normal distribution table or calculator, the probability of z being between -1 and 1 is approximately 0.6826.

Therefore, the answer is C.

Question 14

In a Poisson probability problem, the rate of errors is one every two hours.To find the probability of three defects in four hours, 
A)   = 1, x = 4
B)  = 2, x = 3
C)   = 3, x = 2
D) $\mu$ = 3, x = 6

Accepted Answer

We use the Poisson probability formula: P(x events in t time) = (e^(-rt))*(rt)^x / x!, where r is the rate of events, t is the time, and x is the number of events we want to find the probability of. 
In this case, r=1/2 (since the rate is one error every two hours), t=4 hours (since we want to find the probability of three defects in four hours), and x=3 (since we want to find the probability of three defects). 
Plugging in these values, we get: P(3 defects in 4 hours) = (e^(-2))*(2)^3 / 3! = 0.180447. 
The closest choice to this answer is B, which gives the correct value of r and x, but has the wrong values for t and μ.

Quiz 6: Continuous Probability Distributions

The area of the continuous uniform probability distribution is

There is a lower limit but no upper limit for a random variable that follows the

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes.What is the probability the trip takes more than 40 minutes?

Which of the following probability distributions have the same value for mean, median, and mode?

Which of the following are continuous random variables? I.The weight of an elephant II. The time to answer a questionnaire III.The number of floors in a skyscraper IV.The square feet of countertop in a kitchen

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is speed, measured in miles per hour.This random variable is a

The uniform distribution defined over the interval from 25 to 40 has the probability density function?

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is

The probability distribution that can be described by just one parameter is the

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes.What is the probability the trip takes between 20 and 30 minutes?

In a Poisson probability problem, the rate of errors is one every two hours.To find the probability of three defects in four hours,

Quiz 6: Continuous Probability Distributions

The time it takes to travel from home to the office is normally distributed with μ\muμ = 25 minutes and = 5 minutes.What is the probability the trip takes more than 20 minutes?

The area of the continuous uniform probability distribution is​