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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Baseball A baseball fan examined the record of a favorite baseball player’s performance during his last season. The numbers of games in which the player had zero, one, two, three, and four hits are recorded in the table shown below.

Number of hits 0 1 2 3 4
Frequency 31 58 45 19 5

(a) Complete the table below, where x is the number of hits.

x 0 1 2 3 4
P(x)

(b) Use the table in part (a) to sketch the graph of the probability distribution.

(c) Use the table in part (a) to find   P ( 1 x   3 ) .

(d) Determine the mean and interpret the result in the context of the problem.

(e) Determine the variance and standard deviation.

(a)

To determine

To calculate: The value of P(x) and complete the table.

x01234P(x)

Explanation

Given Information:

The performance table of a baseball player is provided, where number of hits and their frequency is shown

Number of hits01234Frequency315845195

Formula used:

The formula used for probability in this question is

P(x)=Frequency of xNumber of outcomes in S=n(x)n(s)

Where x is a random variable.

Calculation:

Consider the table provided

Number of hits01234Frequency315845195

Let the random variable x is the number of hits by a baseball player in a season.

The sample space will have total 31+58+45+19+5=158 outcomes

Now by using formula

P(x)=Frequency of xNumber of outcomes in S=n(x)n(s)

When,

x=0, P(x

(b)

To determine

To graph: The probability distribution by the table obtained in part (a)

(c)

To determine

To calculate: The probability P(1x3) using the table obtained in part (a), the table obtained is

x01234P(x)311585815845158191585158

(d)

To determine

To calculate: The mean and interpret the result of the discrete random variable x, where x is the number of hits by a baseball player in a season.

(e)

To determine

To calculate: The variance and standard deviation of a discrete random variable x, where x is the number of hits by a baseball player in a season.

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