Question 1

The high school GPAs of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories.
 $$\begin{array} { l l } 
\mathrm { GPA } & f ( x ) \
\hline x < 2.0 & .08 \
2.0 \leq x < 2.5 & .12 \
2.5 \leq x < 3.0 & .35 \
3.0 \leq x < 3.5 & .30 \
3.5 \leq x &
\end{array}$$ 
a.Complete the table to make this a valid probability distribution.
b.What is the probability an applicant's GPA will be below 3.0?
c.What is the probability an applicant's GPA will be 2.5 or above?

Accepted Answer

The answer of The high school GPAs of applicants for...

Question 2

Scores on an endurance test for cardiac patients are normally distributed with μ = 182 and σ = 24.
a.What is the probability a patient will score above 190?
b.What percentage of patients score below 170?
c.What score does a patient at the 75th percentile receive?

Accepted Answer

The answer of Scores on an endurance test for cardiac...

Question 3

A process follows the binomial distribution with n = 8 and p = .3.Find
a.P(x = 3)
b.P(x > 6)
c.P(x ≤ 2)

Accepted Answer

The answer of A process follows the binomial distribution with...

Question 4

A light bulb manufacturer claims his 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 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 his light...

Question 5

A salesperson contacts eight potential customers per day.From past experience,we know that the probability of a potential customer making a purchase is 0.10.
a.Define the random variable in words for this experiment.
b.What is the probability the salesperson will make exactly two sales in a day?
c.What is the probability the salesperson will make at least two sales in a day?
d.What percentage of days will the salesperson not make a sale?
e.What is the expected number of sales per day?
​

Accepted Answer

The answer of A salesperson contacts eight potential customers per...

Question 6

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes.
a.What is the probability the trip takes more than 20 minutes?
b.What is the probability the trip takes less than 15 minutes.
c.What is the probability the trip takes between 30 and 35 minutes?
d.What is the probability the trip takes more than 40 minutes?

Accepted Answer

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

Question 7

Explain how the binomial distribution could be used in quality control to sample 50 parts in a lot of 500.​

Accepted Answer

The answer of Explain how the binomial distribution could be...

Question 8

One way a discrete probability distribution can be portrayed is in a table that lists values for x and f(x).Describe two other ways distributions can be represented.​

Accepted Answer

The answer of One way a discrete probability distribution can...

Question 9

A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained.Following is a record of the number of students in a class of 20 who took the test each number of times.
 $$\begin{array} { l l } 
\text { Students } & \text { Number of Tests } \
\hline 10 & 1 \
7 & 2 \
2 & 3 \
1 & 4
\end{array}$$ 
a.Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.
b.Find the expected value of the number of tests taken.
c.Compute the variance.
d.Compute the standard deviation.

Accepted Answer

The answer of A calculus instructor uses computer aided instruction...

Question 10

The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a mean of 10 minutes.
a.What is the probability that the arrival time between customers will be 7 minutes or less?
b.What is the probability that the arrival time between customers will be between 3 and 7 minutes?
​

Accepted Answer

The answer of The time between arrivals of customers at...

Question 11

A video rental store has two video cameras available for customers to rent.Historically,demand for cameras has followed this distribution.The revenue per rental is $40.If a customer wants a camera and none is available,the store gives a $15 coupon for snacks.
 $$\begin{array} { l l l l } 
\text { Demand } & \text { Relative Frequency } & \text { Revenue } & \text { Cost } \
\hline 0 & .35 & 0 & 0 \
1 & .30 & 40 & 0 \
2 & .20 & 80 & 0 \
3 & .10 & 80 & 15 \
4 & .05 & 80 & 30
\end{array}$$ 
a.What is the expected demand for camera rentals?
b.What is the expected revenue from camera rentals?
c.What is the expected cost associated with camera rentals?
d.What is the expected profit from camera rentals?

Accepted Answer

The answer of A video rental store has two video...

Question 12

The time required to assemble a part of a machine follows an exponential probability distribution with a mean of 14 minutes.
a.What is the probability that the part can be assembled in 7 minutes or less?
b.What is the probability that the part can be assembled between 3.5 and 7 minutes?
​

Accepted Answer

The answer of The time required to assemble a part...

Question 13

The weight of a .5 cubic yard bag of landscape mulch in uniformly distributed over the interval from 38.5 to 41.5 pounds.
a.Give a mathematical expression for the probability density function.
b.What is the probability that a bag will weigh more than 40 pounds?
c.What is the probability that a bag will weigh less than 39 pounds?
d.What is the probability that a bag will weigh between 39 and 40 pounds?

Accepted Answer

The answer of The weight of a .5 cubic yard...

Question 14

Sandy's Pet Center grooms large and small dogs.It takes Sandy 40 minutes to groom a small dog and 70 minutes to groom a large dog.Large dogs account for 20% of Sandy's business.Sandy has 5 appointments tomorrow.
a.What is the probability that all 5 appointments tomorrow are for small dogs?
b.What is the probability that two of the appointments tomorrow are for large dogs?
c.What is the expected amount of time to finish all five dogs tomorrow?

Accepted Answer

The answer of Sandy's Pet Center grooms large and small...

Question 15

Consider a Poisson probability distribution in a manufacturing process with an average of 3 flaws every 100 feet.Find the probability of
a.no flaws in 100 feet
b.2 flaws in 100 feet
c.1 flaws in 150 feet
d.3 or 4 flaws in 150 feet

Accepted Answer

The answer of Consider a Poisson probability distribution in a...

Question 16

A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20.
a.What percentage of its customers has daily balances of more than $275?
b.What percentage of its customers has daily balances less than $243?
c.What percentage of its customers' balances is between $241 and $301.60?
​

Accepted Answer

The answer of A local bank has determined that the...

Question 17

Water's Edge is a clothing retailer that promotes its products via catalog and accepts customer orders by all of the conventional ways including the Internet.The company has gained a competitive advantage by collecting data about its operations and the customer each time an order is processed.
Among the data collected with each order are: number of items ordered,total shipping weight of the order,whether or not all items ordered were available in inventory,time taken to process the order,customer's number of prior orders in the last 12 months,and method of payment.
For each of the six aforementioned variables,identify which of the variables are discrete and which are continuous.

Accepted Answer

The answer of Water's Edge is a clothing retailer that...

Question 18

The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes.
a.What is the probability density function for the time it takes to complete the task?
b.What is the probability that it will take a worker less than 4 minutes to complete the task?
c.What is the probability that it will take a worker between 6 and 10 minutes to complete the task?
​

Accepted Answer

The answer of The time it takes a worker on...

Question 19

After a severe winter,potholes develop in a state highway at the rate of 5.2 per mile.Thirty-five miles of this highway pass through Washington County.
a.How many potholes would you expect to see in the county?
b.What is the probability of finding 8 potholes in 1 mile of highway?

Accepted Answer

The answer of After a severe winter,potholes develop in a...

Question 20

Twenty-five percent of all resumes received by a corporation for a management position are from females.Fifteen resumes will be received tomorrow.
a.Define the random variable in words for this experiment.
b.What is the probability that exactly 5 of the resumes will be from females?
c.What is the probability that fewer than 3 of the resumes will be from females?
d.What is the expected number of resumes from women?
e.What is the variance of the number of resumes from women?
​

Accepted Answer

The answer of Twenty-five percent of all resumes received by...

Quiz 3: Probability Distributions

Scores on an endurance test for cardiac patients are normally distributed with μ = 182 and σ = 24. a.What is the probability a patient will score above 190? b.What percentage of patients score below 170? c.What score does a patient at the 75th percentile receive?

A process follows the binomial distribution with n = 8 and p = .3.Find a.P(x = 3) b.P(x > 6) c.P(x ≤ 2)

Explain how the binomial distribution could be used in quality control to sample 50 parts in a lot of 500.​

One way a discrete probability distribution can be portrayed is in a table that lists values for x and f(x).Describe two other ways distributions can be represented.​

The time required to assemble a part of a machine follows an exponential probability distribution with a mean of 14 minutes. a.What is the probability that the part can be assembled in 7 minutes or less? b.What is the probability that the part can be assembled between 3.5 and 7 minutes? ​

Consider a Poisson probability distribution in a manufacturing process with an average of 3 flaws every 100 feet.Find the probability of a.no flaws in 100 feet b.2 flaws in 100 feet c.1 flaws in 150 feet d.3 or 4 flaws in 150 feet

After a severe winter,potholes develop in a state highway at the rate of 5.2 per mile.Thirty-five miles of this highway pass through Washington County. a.How many potholes would you expect to see in the county? b.What is the probability of finding 8 potholes in 1 mile of highway?

Explain how the binomial distribution could be used in quality control to sample 50 parts in a lot of 500.

One way a discrete probability distribution can be portrayed is in a table that lists values for x and f(x).Describe two other ways distributions can be represented.

The time required to assemble a part of a machine follows an exponential probability distribution with a mean of 14 minutes. a.What is the probability that the part can be assembled in 7 minutes or less? b.What is the probability that the part can be assembled between 3.5 and 7 minutes?