Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
7th Edition
ISBN: 9781337298353
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
Publisher: South-Western College Pub
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Chapter 5, Problem 59SE

The U.S. Coast Guard (USCG) provides a wide variety of information on boating accidents including the wind condition at the time of the accident. The following table shows the results obtained for 4401 accidents (USCG website, November 8, 2012).
Chapter 5, Problem 59SE, The U.S. Coast Guard (USCG) provides a wide variety of information on boating accidents including

Let x be a random variable reflecting the known wind condition at the time of each accident.
Set x = 0 for noir, x = 1 for light, x = 2 for moderate, x = 3 for strong, and x = 4 for storm.
a. a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance and standard deviation for x.
d. Comment on what your results imply about the wind conditions during boating accidents.

a.

Expert Solution
Check Mark
To determine

The probability distribution of x.

Answer to Problem 59SE

The probability distribution is:

    XP(X=x)
    00.096
    10.57
    20.238
    30.077
    40.019

Explanation of Solution

Given:

The results of wind condition at the time of 4401 accident are as given in the following table:

    Wind conditionPercentage of Accident
    None9.6
    Light57
    Moderate23.8
    Strong7.7
    Strom1.9

Formula used:

The formulas are:

  E(X)=i=1nxipi V(X)=E( X 2 ) (E(X)) 2 σ=V(X)

Calculation:

Consider, X be a random variable reflecting the known wind condition at the time of each accident.

Set X = 0 for none, X = 1 for light, X = 2 for moderate, X = 3 for strong, and X = 4 for storm.

That is, X={0,1,2,3,4}

Thus, the required probability distribution of X is −

      X

      P(X=x)

    00.096
    10.57
    20.238
    30.077
    40.019

b.

Expert Solution
Check Mark
To determine

To find:The expected value of X

Answer to Problem 59SE

The expected value of x is 1.353.

Explanation of Solution

Calculation:

The expected value of x can be computed as:

  E(X)=i=1nxipi=0×0.096+1×0.238+3×0.077+4×0.019=1.353

Hence, the expected value of x is 1.353.

c.

Expert Solution
Check Mark
To determine

To find: The standard deviation and variance of x.

Answer to Problem 59SE

The variance and standard deviation of x are 0.68839 and 0.8296 respectively.

Explanation of Solution

Calculation:

The variance and standard deviation of x can be computed as:

  E(X)=i=1nxipi=0×0.096+1×0.238+3×0.077+4×0.019=1.353E(X2)=i=1nx2ipi=02×0.096+12×0.238+32×0.077+42×0.019=2.519V(X)=2.519[1.353]2=0.68839σ=0.68839=0.8296

Hence, the variance and standard deviation of x are 0.68839 and 0.8296 respectively.

d.

Expert Solution
Check Mark
To determine

To explain: The wind condition during boating accidents.

Explanation of Solution

The wind condition during the boating accidents can be understood from the results obtained in part b and c. That is,

On an average the wind condition during the boating accidents is 1.353 and the dispersion or the variance in the wind condition is 0.68839.

In other words, the wind condition on an average is approximately 135.3% and variability of wind condition is nearly 68.839% during the boating accidents.

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