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QUESTION 1

The likelihood distribution of a random variable X is

x–2–1012P ( X = x )

Compute the imply, variance, and commonplace deviation of X.

a.

b.

c.

d.

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QUESTION 2

A likelihood distribution has a imply of 57 and a typical deviation of 1.four. Use Chebychev’s inequality to search out the worth of c that ensures the likelihood is no less than 96% that an end result of the experiment lies between 57 – c and 57 – c. (Spherical the reply to nearest complete quantity.)

a.three

b.9

c.1

d.7

e.5

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QUESTION three

Discover the variance of the likelihood distribution for the histogram:

a.Var ( X) = four.2625

b.Var ( X) = four.65

c.Var ( X) = four.28

d.Var ( X) = four.0125

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QUESTION four

The birthrates within the nation for the years 1981-1990 are:

Yr1981198219831984198519861987198819891990Birthrate15.915.515.515.715.715.615.715.916.216.7

(The birthrate is the variety of stay births/1,000 inhabitants.)

Compute the imply, variance, and commonplace deviation of the random variable X.

a.

b.

c.

d.

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QUESTION 5

Rosa Walters is contemplating investing $10,000 in two mutual funds. The anticipated returns from value appreciation and dividends (in a whole lot of ) are described by the next likelihood distributions:

Mutual Fund A

ReturnsProbability-40.280.3100.5

Mutual Fund B

ReturnsProbability-20.260.680.2

Compute (in ) the imply and variance for every mutual fund.

a. Mutual Fund A:

Mutual Fund B:

b. Mutual Fund A:

Mutual Fund B:

c. Mutual Fund A:

Mutual Fund B:

d. Mutual Fund A: Mutual Fund B:

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QUESTION 6

The variety of Individuals with out medical insurance, in tens of millions, from 1995 by way of 2002 is summarized within the following desk.

Yr19951996199719981999200020012002Individuals40.541.443.644.740.239.241.143

What’s the commonplace deviation of Individuals with out medical insurance within the interval from 1995 by way of 2002?

a. million

b. million

c. million

d. million

e. million

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QUESTION 7

The imply annual beginning wage of a brand new graduate in a sure career is $43,000 with a typical deviation of $500. What’s the likelihood that the beginning wage of a brand new graduate on this career shall be between $39,500 and $46,500?

a.At the least

b.At the least

c.At the least

d.At the least

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QUESTION eight

A survey was performed by the market analysis division of the Nationwide Actual Property Firm amongst 500 potential consumers in a big metropolitan space to find out the utmost value a potential purchaser could be prepared to pay for a home. From the information collected, the distribution that follows was obtained.

Compute the usual deviation of the utmost value (in 1000’s of ) that these consumers had been prepared to pay for a home. Spherical the reply to the closest integer.

Most Worth Thought-about, 150160170180190220250270320

a.

b.

c.

d.

e.

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QUESTION 9

The next desk provides the scores of 30 college students in a arithmetic examination.

Scores90-9980-8970-7960-6950-59College students381351

Discover the imply and the usual deviation of the distribution of the given knowledge. Trace: Assume that each one scores mendacity inside a gaggle interval take the midvalue of that group.

a.

b.

c.

d.

e.

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QUESTION 10

A likelihood distribution has a imply of 45 and a typical deviation of 1. Use Chebychev’s inequality to estimate the likelihood that an end result of the experiment lies between 43 and 47.

a.At the least zero.eight

b.At the least zero.75

c.At the least zero.5

d.At the least zero.25

e.At the least zero.04

Two

QUESTION 1

Discover the worth of the likelihood of the usual regular variable Z comparable to the shaded space beneath the usual regular curve.

P ( – 1.36 < Z < 1.75 )

a.P (- 1.36 < Z < 1.75 ) = zero.0869

b.P (- 1.36 < Z < 1.75 ) = zero.8730

c.P (- 1.36 < Z < 1.75 ) = zero.9599

d.P (- 1.36 < Z < 1.75 ) = 1.0468

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QUESTION 2

Suppose X is a traditional random variable with and . Discover the worth of .

a.zero.9050

b.zero.8996

c.zero.8945

d.zero.8818

e.zero.9857

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QUESTION three

Discover the worth of the likelihood of the usual regular variable Z comparable to this space.

P ( Z > 2.31 )

a.P ( Z > 2.31 ) = zero.0084

b.P ( Z > 2.31 ) = zero.0104

c.P ( Z > 2.31 ) = zero.0136

d.P ( Z > 2.31 ) = zero.9896

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QUESTION four

Suppose X is a traditional random variable with and . Discover the worth of .

a.zero.498

b.zero.726

c.zero.495

d.zero.4333e.zero.72

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QUESTION 5

Discover the worth of the likelihood of the usual regular variable Z comparable to the shaded space beneath the usual regular curve.

P ( zero.three < Z < 1.85 )

a.P (zero.three < Z < 1.85 ) = zero.3499

b.P (zero.three < Z < 1.85 ) = 1.5857

c.P (zero.three < Z < 1.85 ) = zero.9678

d.P (zero.three < Z < 1.85 ) = zero.6179

Three

QUESTION 1

In accordance with knowledge launched by the Chamber of Commerce of a sure metropolis, the weekly wages (in ) of feminine manufacturing facility staff are usually distributed with a imply of 575 and a typical deviation of 50. Discover the likelihood feminine manufacturing facility employee chosen at random from town makes a weekly wage of $550 to $625.

a.The likelihood is zero.5438.

b.The likelihood is zero.5328.

c.The likelihood is zero.4297.

d.The likelihood is zero.5339.

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QUESTION 2

To be eligible for additional consideration, candidates for sure Civil Service positions should first go a written qualifying examination on which a rating of 70 or extra should be obtained. In a latest examination it was discovered that the scores had been usually distributed with a imply of 67 factors and a typical deviation of 6 factors. Decide the proportion of candidates who handed the written qualifying examination.

a.18.79% candidates handed the written qualifying examination.

b.19.52% candidates handed the written qualifying examination.

c.30.85% candidates handed the written qualifying examination.

d.24.74% candidates handed the written qualifying examination.

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QUESTION three

Use the suitable regular distribution to approximate the ensuing binomial distribution.

The supervisor of Madison Finance Firm has estimated that, due to a recession yr, 5% of its 400 mortgage accounts shall be delinquent. If the supervisor’s estimate is appropriate, what’s the likelihood that 11 or extra of the accounts shall be delinquent?

a.The likelihood is zero.9994.

b.The likelihood is zero.9891.

c.The likelihood is zero.8137.

d.The likelihood is zero.9854.

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QUESTION four

Use the suitable regular distribution to approximate the ensuing binomial distribution.

A basketball participant has a 75% likelihood of creating a free throw. What’s the likelihood of her making 80 or extra free throws in 120 trials?

a.The likelihood is zero.9744.

b.The likelihood is zero.9822.

c.The likelihood is zero.9864.

d.The likelihood is zero.9898.

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QUESTION 5

Use the suitable regular distribution to approximate the ensuing binomial distribution.

Colorado Mining and Mineral has 800 workers engaged in its mining operations. It has been estimated that the likelihood of a employee assembly with an accident throughout a 1-year interval is .1. What’s the likelihood that greater than 80 staff will meet with an accident in the course of the 1-year interval?

a.The likelihood is zero.4684.

b.The likelihood is zero.4669.

c.The likelihood is zero.8491.

d.The likelihood is zero.4761.

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