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[answered] 1.Determine the mean and standard deviation of the variable


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1.Determine the mean and standard deviation of the variable X in the binomial distribution where n=55 and ?=0.90.

 

Determine the mean. ?= nothing (Type an integer or a decimal.) Determine the standard deviation.

 

?=

 

nothing (Round to three decimal places as needed.) 2.Do males or females feel more tense or stressed out at work? A survey of employed adults conducted online by a company on behalf of a research organization revealed the data in the contingency table shown to the right. Complete parts (a) through (d) below. Felt Tense or Stressed Out at Work

 

GenderYes No Total

 

Male 245 355 600

 

Female400 230 630

 

Total 645 585 1230 a. What is the probability that a randomly selected person's gender is female?

 

nothing (Type an integer or a decimal. Round to three decimal places as needed.)

 

b. What is the probability that a randomly selected person feels tense or stressed out at work and is female?

 

nothing (Type an integer or a decimal. Round to three decimal places as needed.)

 

c. What is the probability that a randomly selected person feels tense or stressed out at work or is female?

 

nothing (Type an integer or a decimal. Round to three decimal places as needed.)

 

d. Explain the difference in the results in (b) and (c).

 

A.The two characteristics in part (b) are collectively exhaustive, while those in part (c) are not.

 

B.The two characteristics in part (b) are mutually exclusive, while those in part (c) are not.

 

C.The joint event in part (c) includes the possibility that just one of the two characteristics occurs.

 

3.Suppose that E and F are two events and that P (E and F) = 0.1 and P (E) = 0.5. What is P(F|E)? P(F|E)= nothing (Type an integer or a decimal. Do not round.)

 

4.A student is taking a multiple?choice exam in which each question has two choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place two balls (marked A and B) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are nine multiple?choice questions on the exam. Complete parts (a) through (d) below.

 

a. What is the probability that she will get nine questions correct?

 

nothing (Round to four decimal places as needed.) b. What is the probability that she will get at least eight questions correct?

 

nothing (Round to four decimal places as needed.) c. What is the probability that she will get no questions correct?

 

nothing (Round to four decimal places as needed.) d. What is the probability that she will get no more than two questions correct?

 

nothing (Round to four decimal places as needed.) 5.If P(A)equals=0.6, P(B)=0.3, and (A and B)equals=0.18, are A and B independent?

 

A.Yes

 

B.No

 

C.Not enough information

 

6.The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) are shown to the right.

 

a. Compute the expected number of mortgages approved per week.

 

b. Compute the standard deviation. a. The expected number of mortgages approved per week is Number Approved

 

0

 

1

 

2

 

3

 

4

 

5

 

6

 

7 Frequency

 

121

 

252

 

323

 

171

 

8

 

7

 

2

 

1 nothing .(Round to three decimal places as needed.) b. The standard deviation is nothing .(Round to three decimal places as needed.) 7.Use the contingency table below to find the followingprobabilities.

 

a. A|B

 

b. A|B'

 

c. A'|B'

 

d. Are events A and B independent?

 

a.P(A|B)= nothing B B' (Round to two decimal places as needed.) b.P(A|B')= nothing (Round to two decimal places as needed.)

 

c.P(A'|B')= nothing (Round to two decimal places as needed.

 

d. Are events A and B independent? and B are independent.

 

A and B are not independent. 8.You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The information to the right about the annual return (per $1,000) of each of these investments Economic

 

under different economic conditions is available, along with ProbabilityCondition

 

the probability that each of these economic conditions will occur. Complete parts (a) through (c) below.

 

0.01

 

Extreme recession

 

0.09

 

Recession

 

0.20

 

Stagnation

 

0.30

 

Slow growth

 

0.35

 

Moderate growth

 

0.05

 

High growth Corporate Common

 

Bond Stock Fund

 

Fund ?250

 

?999 ?60 30

 

80 ?300

 

?150

 

150 100 200 110 350 a. Compute the expected return for the corporate bond fund and for the common stock fund.

 

The expected return for the corporate bond fund is nothing .(Round to two decimal places as needed.)

 

The expected return for the common stock fund is nothing . (Round to two decimal places as needed.) b. Compute the standard deviation for the corporate bond fund and for the common stock fund.

 

The standard deviation for the corporate bond fund is nothing .(Round to two decimal places as needed.) The standard deviation for the common stock fund is nothing .(Round to two decimal places as needed.) c. Would you invest in the corporate bond fund or the common stock fund? Explain.

 

Based on the expected value, the corporate bond or common stock fund should be chosen. Since the standard deviation for the common stock fund is more than three times greater than or about the same as or less than half as much as that for the corporate bond fund, the common stock fund is safer than or is riskier than or has the same risk as the corporate bond fund and an investor doesn't need to consider or should carefully weigh the risk when making a decision. 9.The following is a set of data for a population with N=10.

 

10 3 1??12??15??5??11? 11??9??7?? a. Compute the population mean.

 

b. Compute the population standard deviation.

 

a. The population mean is ?=

 

nothing . (Type an integer or a decimal. Do not round.) b. The population standard deviation is ?=

 

(Round to two decimal places as needed.) nothing . 10.The market capitalizations of 20 companies, in billions of dollars, are listed to the right. Complete parts (a) and (b). 159.6 170.3 156.8 172.1 165.3 168.2 161.9 150.9 151.2 153.3

 

156.7 162.4 155.3 155.7 139.3

 

130.3 186.3 182.1 125.3 201.4

 

a. Calculate the mean and standard deviation of the market capitalization for this population of 20 companies.

 

The mean is ?=

 

nothing . (Round to three decimal places as needed.) The standard deviation is ?=

 

nothing .(Round to three decimal places as needed.) b. Interpret the parameters calculated in (a). Choose the correct answer below.

 

A.The standard deviation is Large as a portion of the mean. This indicates that the values are relatively concentrated.

 

B.The standard deviation is smallas a portion of the mean. This indicates that the values are relatively spread out.

 

C.The standard deviation is large as a portion of the mean. This indicates that the values are relatively spread out.

 

D.The standard deviation is Small as a portion of the mean. This indicates that the values are relatively concentrated. 0 %

 


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