QNT 275T Week 3 Apply Week 3 Case(New)

A multiple-choice test has 30 questions and each one has five possible answers, of which only one is correct. If all answers were guesses, find the probability of getting exactly four correct answers.

.0604

.1325

.2552

.8000

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?

❏ .6321

❏ .5507

❏ .7135

❏ .4493

Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it between 50 feet and 60 feet?

❏ .9972

❏ .5000

❏ .9544

❏ .4772

An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that all five will be repaired on the same day?

.0010

.6328

.9990

.2373

4.

Award: 1 out of 1.00 point

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective?

0.2250

0.3000

0.0250

0.4000

0.1500

5.

Award: 1 out of 1.00 point

The probability of event A occurring given that event B has already occurred is 0.61. The probability of both events occurring is 0.5. What is the probability of event B occurring?

0.305

0.195

0.390

0.820

0.500

6.

Award: 1 out of 1.00 point

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X ≤ 1).

rev: 01_31_2019_QC_CS-156253

.0870

.2592

.0778

.3370

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the variance.

5.0

1.2

2.0

1.1

7.

Award: 0 out of 1.00 point

A family has two children. What is the probability that both are girls, given that at least one is a girl?

1/8

1/4

1/2

1/3

1/6

8.

Award: 1 out of 1.00 point

A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn is a vowel?

5/26

1/26

4/26

21/26

9.

Award: 1 out of 1.00 point

If n = 15 and p = .4, then the standard deviation of the binomial distribution is

9.

6.

3.6.

1.897.

.4.

10.

Award: 1 out of 1.00 point

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

.79

.45

.55

.50

Employees of a local university have been classified according to gender and job type.

A(n) ______________ is a collection of sample space outcomes.

experiment

event

set

probability

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain more than 2.50 ounces?

.9525

.4525

.0475

.5474

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of more than 7 customers arriving within a minute.

.0216

.0081

.0108

.0118

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the expected value of X.

3

9

1.5

1.7

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). What is the standard deviation for this distribution?

1.5

1.22

0.75

0.87

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.

Are D and C mutually exclusive?

Yes, mutually exclusive.

No, not mutually exclusive.

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?

34.48

21.68

38.32

25.52

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?

.6321

.5507

.7135

.4493

If the mileage per gallon for a car is normally distributed, 32 mpg has a z score of 1.2, and 24 mpg has a z score of −.4, what is the mean mpg of the distribution?

28

26

30

38

If the random variable x is normally distributed, ______ percent of all possible observed values of x will be within three standard deviations of the mean.

68.26

95.44

99.73

100

None of the other choices is correct.

A continuous probability distribution that is useful in describing the time or space between successive occurrences of an event is a(n)

uniform probability distribution.

normal probability distribution.

Poisson probability distribution.

exponential probability distribution.

A probability may be interpreted as a long-run _____________ frequency.

observational

relative

experimental

conditional

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a male Republican.

.125

.500

.333

.667

.188

If an employee is selected at random, what is the probability that the employee is a member of the hourly staff, given that the employee is female?

0.400

0.133

0.160

0.053

0.533

The probability that an appliance is currently being repaired is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 are currently being repaired? Use the normal approximation to the binomial.

.5000

.0287

.6000

.9713

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What is the probability that the wine cooler would be greater than 60 degrees?

Do NOT include % symbol with your response. Answer format: ##.

What is the probability that the wine cooler would be less than 45 degrees?

Do NOT include % symbol with your response. Answer format: ##.

What is the percentage of wine coolers served at the ideal temperature, between 49 and 55 degrees?

Do NOT include % symbol with your response. Answer format: ##.

What is the probability that at least 5 six packs will be bought in a month?

Do NOT include % symbol with your response. Answer format: ##.

Based on the probabilities for the ratings of 4 and 5, which age/gender demographic would be the best target audience for the new concept?

Women age 21-24

Women age 25-34

Men age 25-34

Men age 21-24

What is the probability that exactly 3 six packs will be bought in a month?

Do NOT include % symbol with your response. Answer format: ##.

What is the probability that between 4 and 8 six packs will be bought in a month?

Do NOT include % symbol with your response. Answer format: ##.

QNT 275 Week 3 Apply: Connect Week 3 Case

Three hundred consumers between 21 and 49 years old were randomly selected. After sampling a new wine cooler, each was asked to rate the appeal of the phrase: “Not sweet like wine coolers, not filling like beer, and more refreshing than wine or mixed drinks” as it relates to the new wine cooler. The rating was made on a scale from 1 to 5, with 5 representing “extremely appealing” and with 1 representing “not at all appealing”.

As a manager overseeing the development of the concept, you bottle the wine cooler and placed it into distribution in one test store.

Your manager has asked you to assess the data and determine the most likely customer based on the ratings. Additionally, your manager would like you to review sales in the test store.

Use the Week 3 Data Set to create and calculate the following in Excel®:

1. Estimate the probability that a randomly selected 21 to 49 year old consumer:

   • Would give the phrase a rating of 5
   • Would give the phrase a rating of 3 or higher
   • Is in the 21-24 age group
   • Is a male who gives the phrase a rating of 4
   • Is a 35 to 49 year old who gives the phrase a rating of 1
   • Based on the probabilities for the ratings of 4 and 5, which age/gender demographic would be the best target audience for the new concept?

2. Create a probability distribution using the data which shows how many cartons of the wine cooler were bought per customer in a month.

   • Calculate the mean and the standard deviation of your probability distribution.
   • Calculate the probability that exactly 3 six packs will be bought in a month.
   • Calculate the probability that between 4 and 8 six packs will be bought in a month.
   • Calculate the probability that at least 5 six packs will be bought in a month.
   • Calculate the probability that no more than 5 six packs will be bought in a month.

3. Create a relative frequency distribution based on the wine cooler drinking temperatures.

   • Create 6 bins with the same interval in each.
   • Create a histogram

4. Considering the mean and standard deviation for the ideal drinking temperature:

   • Calculate z values then refer to Table 6.1 – Cumulative Areas Under the Standard Normal Curve
   • Calculate the probability of the wine cooler being less than 45 degrees.
   • Calculate the probability of the wine cooler being greater than 60 degrees.
   • Calculate the percentage of wine coolers served at the ideal temperature, between 49 and 55 degrees.

Click the Assignment Files tab to submit.

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