1. Section 5.2, Exercise 1

Suppose 20% of the people in a city prefer Pepsi-Cola as their soft drink of choice. If a random sample of six people is chosen, the number of Pepsi drinkers could range from zero to six. Shown here are the possible numbers of Pepsi drinkers in a sample of six people and the probability of that number of Pepsi drinkers occurring in the sample. Use the data to determine the mean number of Pepsi drinkers in a sample of six people in the city and compute the variance and standard deviation.

 

Number of Pepsi Drinkers	Probability
0	0.262
1	0.393
2	0.246
3	0.082
4	0.015
5	0.002
6	0.000

 

 

µ =

s2 =

s =

Round your answer to 3 decimal places.

 

The tolerance is +/- 0.005.

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Please read and follow the instruction:

 

1. Subject name Statistics for Managerial Decisions

2. I have 8 question (All questions have 3 or 4 Sub questions)

3. It's mathematical calculation Paper

 

#Important:

  I give you 2 PowerPoint slide, those are help you to find the answers.

 

(If you have any question email me or message me as soon as possible)

 

 

1. Section 5.2, Exercise 1

Suppose 20% of the people in a city prefer Pepsi-Cola as their soft drink of choice. If a random sample of six people is chosen, the number of Pepsi drinkers could range from zero to six. Shown here are the possible numbers of Pepsi drinkers in a sample of six people and the probability of that number of Pepsi drinkers occurring in the sample. Use the data to determine the mean number of Pepsi drinkers in a sample of six people in the city and compute the variance and standard deviation.

 μ =

 σ2 =

 σ =

Round your answer to 3 decimal places.

The tolerance is +/- 0.005.

 

 

2. Section 5.3, Exercise 1

The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for “slightly higher pay.” In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for “slightly higher pay.

What is the probability that nine or more say yes?

What is the probability that three, four, five, or six say yes?

If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates?

What is the probability that all of the companies say there is a shortage of qualified job candidates?

What is the expected number of companies that would say there is a shortage of qualified job candidates?

Round your answer to 3 decimal places.

The tolerance is +/- 0.005

 

 

 

3. Section 5.4, Exercise 7

A service station has a pump that distributes diesel fuel to automobiles. The station owner estimates that only about 3.2 cars use the diesel pump every 2 hours. Assume the arrivals of diesel pump users are Poisson distributed.

a. What is the probability that three cars will arrive to use the diesel pump during a 1-hour period?

b. Suppose the owner needs to shut down the diesel pump for half an hour to make repairs. However, the owner hates to lose any business. What is the probability that no cars will arrive to use the diesel pump during a half-hour period?

c. Suppose five cars arrive during a 1-hour period to use the diesel pump. What is the probability of five or more cars arriving during a 1-hour period to use the diesel pump?

Round your answer to 4 decimal places.

The tolerance is +/- 0.0005.

 

4. Section 5.3, Exercise 9

In the past few years, outsourcing overseas has become more frequently used than ever before by U.S. companies. However, outsourcing is not without problems. A recent survey by Purchasing magazine indicates that 20% of the companies that outsource overseas use a consultant. Suppose 15 companies that outsource overseas are randomly selected.

a. What is the probability that exactly five companies that outsource overseas use a consultant?
b. What is the probability that more than ten companies that outsource overseas use a consultant?
c. What is the probability that none of the companies that outsource overseas use a consultant?
d. What is the probability that between four and seven (inclusive) companies that outsource overseas use a consultant?
e. Construct a graph for this binomial distribution.

*Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places, the tolerance is +/-0.0005.
**Round your answer to 3 decimal places when calculating using Table A.2.

a. P(x = 5) = 

*
b. P(x > 10) = 

**
c. P(x = 0) = 

*
d. P(4 ≤ x ≤ 7) = 

**

e. Choose the correct graph below.

A)		C)
B)		D)

 

 

 

 

 

 

5. Section 6.1, Exercise 1

According to the Australian Tax Office, income tax returns one year averaged $1,332 in refunds for taxpayers. One explanation of this figure is that taxpayers would rather have the government keep back too much money during the year than to owe it money at the end of the year. Suppose the average amount of tax at the end of a year is a refund of $1,332, with a standard deviation of $725. Assume that amounts owed or due on tax returns are normally distributed.
(a) What proportion of tax returns show a refund greater than $2,000?
(b) What proportion of the tax returns show that the taxpayer owes money to the government?
(c) What proportion of the tax returns show a refund between $100 and $700?

Round z values to 2 decimal places. Round your answers to 4 decimal places, the tolerance is +/-0.0001

(a)
P(X > $2000) =

 

(b)
P(X < 0) =

 

(c)
P($100 < X < $700) =

 

 

 

 

6. Section 6.1, Question 20

Suppose X is normally distributed with a standard deviation of 7. Seventy-one percent of the values are less than 45. The mean is:

 

43.53

 

46.47

 

41.15

 

48.85

 

 

 

 

7. Section 6.5, Exercise 7 According to the U.S. Department of Labor, the average American household spends $639 on household supplies per year. Suppose annual expenditures on household supplies per household are uniformly distributed between the values of $233 and $1,045. (a) What is the standard deviation of this distribution? (b) What is the height of this distribution? (c) What proportion of households spend more than $800 per year on household supplies? (d) What proportion of households spend more than $1,260 per year on household supplies? (e) What proportion of households spend between $380 and $490 on household supplies? *Round your answers to 4 decimal places, the tolerance is +/-0.0005. **Round your answers to 4 decimal places. (a) Standard deviation =  * (b) Height =  * (c) P(x > 800) =  * (d) P(x > 1,260) =  ** (e) P(380 < x < 490) =  *

 

 

 

 

 

 

 

8. Section 6.6, Exercise 3

During the summer at a small private airport in Far-North Queensland, the unscheduled arrival of airplanes is Poisson distributed with an average arrival rate of 1.12 planes per hour.
(a) What is the average interarrival time between planes?
(b) What is the probability that at least 2 hours will elapse between plane arrivals?
(c) What is the probability of two planes arriving less than 10 minutes apart?

(a)
μ =

 min., round your answer to 2 decimal places, the tolerance is +/-0.01

(b)
P(X ≥ 2 hrs| λ = 1.12 planes/hr.) =

, round your answer to 3 decimal places, the tolerance is +/-0.001

(c)
P(X < 10 min| λ = 1.12/hr.) =

, round your answer to 3 decimal places, the tolerance is +/-0.001