Question 1

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

Accepted Answer

A) uniform 
B) normal 
C) exponential 
D) binomial

Question 2

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

Accepted Answer

A) different for each interval 
B) the same for each interval 
C) Either a or b could be correct depending on the magnitude of the standard deviation. 
D) None of the alternative answers is correct.

Question 3

Larger values of the standard deviation result in a normal curve that is

Accepted Answer

A) shifted to the right 
B) shifted to the left 
C) narrower and more peaked 
D) wider and flatter

Question 4

The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 40 minutes.
a.Define the random variable in words.
b.What is the probability of tuning an engine in 30 minutes or less?
c.What is the probability of tuning an engine between 30 and 35 minutes?

Accepted Answer

The answer of The time it takes to completely tune...

Question 5

A light bulb manufacturer claims its light bulbs will last 500 hours on the average. The lifetime of a light bulb is assumed to follow an exponential distribution.
a. What is the probability that the light bulb will have to be replaced within 500 hours?
b. What is the probability that the light bulb will last more than 1000 hours?
c. What is the probability that the light bulb will last between 200 and 800 hours.

Accepted Answer

The answer of A light bulb manufacturer claims its light...

Question 6

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is

Accepted Answer

A) 0.000 
B) 0.0055 
C) 0.4945 
D) 0.9945

Question 7

For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is

Accepted Answer

A) 0.4000 
B) 0.0146 
C) 0.0400 
D) 0.5000

Question 8

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1112?

Accepted Answer

A) 0.3888 
B) 1.22 
C) 2.22 
D) 3.22

Question 9

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces.
a.What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces?
b.What percentage of the items weighs between 4.8 and 5.04 ounces?
c.Determine the minimum weight of the heaviest 5% of all items produced.
d.If 27,875 of the items of the entire production weigh at least 5.01 ounces, how many items have been produced?

Accepted Answer

The answer of The weights of items produced by a...

Question 10

Exhibit 6-7
 
-Refer to Exhibit 6-7. The probability that x is between 3 and 6 is

Accepted Answer

A) 0.4512 
B) 0.1920 
C) 0.2592 
D) 0.6065

Question 11

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. The probability of a player weighing less than 250 pounds is

Accepted Answer

A) 0.4772 
B) 0.9772 
C) 0.0528 
D) 0.5000

Question 12

The probability density function for a uniform distribution ranging between 2 and 6 is

Accepted Answer

A) 4 
B) undefined 
C) any positive value 
D) 0.25

Question 13

Exhibit 6-4
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
-Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?

Accepted Answer

A) 0.4332 
B) 0.9332 
C) 0.0668 
D) 0.5000

Question 14

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The expected assembly time (in minutes) is

Accepted Answer

A) 16 
B) 2 
C) 8 
D) 4

Question 15

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players?

Accepted Answer

A) 196 
B) 151 
C) 249 
D) None of the alternative answers is correct.

Question 16

Exhibit 6-5
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh more than 10 ounces?

Accepted Answer

A) 0.3413 
B) 0.8413 
C) 0.1587 
D) 0.5000

Question 17

The time at which the mailman delivers the mail to Ace Bike Shop follows a normal distribution with mean 2:00 PM and standard deviation of 15 minutes.
a. What is the probability the mail will arrive after 2:30 PM?
b. What is the probability the mail will arrive before 1:36 PM?
c. What is the probability the mail will arrive between 1:48 PM and 2:09 PM?

Accepted Answer

The answer of The time at which the mailman delivers...

Question 18

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.
a.Define the random variable in words.
b.What is the probability that a randomly selected bill will be at least $39.10?
c.What percentage of the bills will be less than $16.90?
d.What are the minimum and maximum of the middle 95% of the bills?
e.If twelve of one day's bills had a value of at least $43.06, how many bills did the restaurant collect on that day?

Accepted Answer

The answer of The daily dinner bills in a local...

Question 19

For a uniform probability density function, the height of the function

Accepted Answer

A) can not be larger than one 
B) is the same for each value of x 
C) is different for various values of x 
D) decreases as x increases

Question 20

The weekly earnings of fastfood restaurant employees are normally distributed with a mean of $395. If only 1.1% of the employees have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the employees?

Accepted Answer

The answer of The weekly earnings of fastfood restaurant employees...

Exam 6: Continuous Probability Distributions