Introduction to Business Statistics
Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Chapter 7, Problem 7.63CE

According to a recent survey, 35% of the adult citizens of Mayville have a charge account at Marcy’s Department Store. Mr. Marcy’s nephew is going to trial for embezzlement, and nine jurors are to be randomly selected from the adult citizenry. What is the probability that at least four of the jurors will be charge-account holders?

Expert Solution & Answer
Check Mark
To determine

The probability value that at least four of the jurors will be charge account holders.

Answer to Problem 7.63CE

The probability value is calculated as 0.4033.

Explanation of Solution

Given information:

  n=9π=0.35

Formula used:

The mean of the distribution is calculated by using the following formula:

  μ=nπ

Where,

Mean: μ

Number of trials: Mean: n

The standard deviation of the distribution is calculated by using the following formula:

  σ=nπ(1π)

The z score is calculated by using the following expression:

  z=xμσ

Where,

The distance from mean measured in standard deviation units: z

Mean: μ

Standard deviation: σ

By using standardized normal table, the probability value of P(z0.2448) is given by 0.5968.

Calculation:

The mean of the distribution:

  μ=nπμ=(9)(0.35)μ=3.15

The standard deviation of the distribution is:

  σ=nπ( 1π)σ=(9)( 0.35)( 10.35)σ=2.0475σ=1.43

To find out the probability value of P(z4), need to use the correction for continuity by changing its interval gap as P(z3.5)

The value of z can be calculated by using following formula:

  z=xμσz=3.503.151.43z=0.2448

By using the standardized normal distribution table to calculate the probability value that x is larger than 3.5 :

  P(z0.2448)=1P(z0.2448)P(z0.2448)=10.5968P(z0.2448)=0.4033

Conclusion:

Therefore, the probability value is 0.4033.

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Chapter 7 Solutions

Introduction to Business Statistics

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