The time it takes a mechanic to change the oil in a car is exponentially distrib
ID: 3336274 • Letter: T
Question
The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 4 minutes. What is the probability that it will take a mechanic less than 4 minutes to change the oil?
0.4512
0.5000
0.6321
0.6988
3.5 points
QUESTION 2
Which of the following is not a property of a binomial experiment?
The experiment consists of a sequence of n identical trials.
Two outcomes referred to as a success or a failure are possible on each trial.
The probability of a failure does not change from one trial to the next.
The trials are dependent.
3.5 points
QUESTION 3
X is a random variable with the probability function: f(X) = X/12 for X = 3, 4 or 5
The expected value of X is
2.33
4
4.17
12
3.5 points
QUESTION 4
For the standard normal probability distribution, the area to the left of the mean is
equal to the area to the right of the mean
0.5
1.0
Both a. and b. are correct.
3.5 points
QUESTION 5
Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is
0.40
1.92
12.00
20.00
3.5 points
QUESTION 6
In a standard normal distribution, the range of values of z is from
-3.09 to 3.09
-1 to 1
0 to 1
3.5 points
QUESTION 7
The number of female customers that enter a bank in an hour is an example of
a continuous random variable
a discrete random variable
either a continuous or a discrete random variable, depending on the number of the customers
either a continuous or a discrete random variable, depending on the gender of the customers
3.5 points
QUESTION 8
A major credit card company has determined that its customers charge an average of $280 per month on their accounts with a standard deviation of $20. What percentage of the customers charges more than $265 per month?
99.38%
77.34%
40.13%
22.66%
3.5 points
QUESTION 9
The weight of an object is an example of
a continuous random variable
a discrete random variable
either a continuous or a discrete random variable, depending on the weight of the object
either a continuous or a discrete random variable, depending on the units of measurement
3.5 points
QUESTION 10
A sample of 100 people was asked how many cups of coffee they drink in the morning. You are given the following sample information:
Cups of Coffee
Frequency
0
30
1
45
2
20
3
5
100
The expected number of cups of coffee is
1.0
1.5
2.0
2.5
3.5 points
QUESTION 11
On the average, 1,234 students check in at the student recreation center every day. Define the random variable X to be the number of students checking in in any day. What is the appropriate probability distribution for X?
binomial probability distribution
uniform probability distribution
Poisson probability distribution
hypergeometric probability distribution
3.5 points
QUESTION 12
Consider a probability density function for a uniform distribution ranging between 2 and 6. What is P(1 x 3)?
0.25
0.50
0.75
1.00
3.5 points
QUESTION 13
The student body of a large university consists of 43% female students. A random sample of 4 students is selected. What is the probability that among the students in the sample exactly two are female?
0.3560
0.3604
0.3643
None of these alternatives is correct.
3.5 points
QUESTION 14
Consider a Poisson probability distribution with µ = 0.4. The variance of this distribution is
0.16
0.40
0.60
1.00
3.5 points
QUESTION 15
Z-scores provide information about the location of raw scores
below the mean in units of the range of the distribution
above the mean in units of the standard deviation of the distribution
above and below the mean in units of the range of the distribution
above and below the mean in standard deviation units from the mean
3.5 points
QUESTION 16
The probability that Peter will catch fish when he goes fishing is 0.7. Peter is going to fish 3 days next week. Define the random variable X to be the number of days Peter catches fish. The expected number of days Peter will catch fish is ________ while the variance of the number of days Peter will catch fish is ________.
0.7, 2.1
2.1, 0.63
2.1, 0.7
0.63, 2.1
3.5 points
QUESTION 17
What area under the standard normal curve falls outside the Z values -2.3 and 2.3?
0.0107
0.0214
0.9786
0.9893
3.5 points
QUESTION 18
When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a
normal probability distribution
binomial probability distribution
hypergeometric probability distribution
Poisson probability distribution
3.5 points
QUESTION 19
A sample of 100 people was asked how many cups of coffee they drink in the morning. You are given the following sample information:
Cups of Coffee
Frequency
0
35
1
40
2
15
3
10
100
The probability that a person from this sample drinks at least two cups of coffee in the morning is
0.10
0.15
0.20
0.25
3.5 points
QUESTION 20
The expected value of a discrete random variable
is a measure of central location of the random variable
is always equal to the median value of the random variable
is a description of the distribution of the values of a random variable and their associated probabilities
None of these alternatives is correct.
3.5 points
QUESTION 21
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n)
normal probability distribution
exponential probability distribution
Poisson probability distribution
uniform probability distribution
3.5 points
QUESTION 22
For a standard normal distribution, a zero value of z indicates that
a mistake has been made in computations, since Z cannot be zero
the sample mean is smaller than the population mean
the sample mean is larger than the population mean
the actual data value is equal to the sample mean
3.5 points
QUESTION 23
For a continuous random variable x, the height of the function at x is
a value less than zero
named the probability density function f(x)
the probability at a given value of x
0.50, since it is the middle value
3.5 points
QUESTION 24
If a normal distribution has mean 100 and standard deviation 5, find K so that the probability that a sample value is less than K is .975. (Choose the closest.)
108
110
112
114
3.5 points
QUESTION 25
Which of the following statements about a discrete random variable and its probability distribution is false?
Values of the discrete random variable can be either a finite number of values or an infinite sequence of values.
Negative values of f(x) are not allowed even though f(x) = 1.
Values of f(x) can be anything (greater than or less than or equal to zero).
All of these alternatives are true statements about a discrete random variable.
3.5 points
QUESTION 26
In a binomial experiment the probability of success is 0.4. What is the probability of three successes in five trials?
0.0006
0.0142
0.2304
0.3456
3.5 points
QUESTION 27
The distribution of lifetimes for a certain type of light bulb is normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the 33rd percentile of the distribution of lifetimes.
456
478
500
956
3.5 points
QUESTION 28
Compute the hypergeometric probabilities for the value of n = 4 and x = 2. Assume N = 8 and r = 5.
0.0000
0.1786
0.4286
0.8571
3.5 points
QUESTION 29
A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is
the same for each interval
different for each interval
equal to 100
at least one
3.5 points
QUESTION 30
If each of a set of raw scores is transformed into a Z-score, the new distribution will have a standard deviation equal to
one
the standard deviation of the original distribution
zero
the mean of the original distribution
a.0.4512
b.0.5000
c.0.6321
d.0.6988
Explanation / Answer
Question 1
ans: Let X be the time it takes for the mechanic to change the oil inthe car. Then X has an exponential distribution with parameter; X~Exp(=1/ = 1/4 = 0.25).
P(X < 4) = 1 - P(X > 4) = 1 - e-x = 1 -e-(0.25)(4) = 1 - 0.367879 = 0.6321
option c. 0.6321 is the right answer
Question 2:
Which of the following is not a property of a binomial experiment
ans:The trials are independent - the outcome of any trial has no effect on the probability of the others
so option d. The trials are dependent.
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