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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 53-56, use a normal approximation.

Management Suppose that a particular Walgreens estimates that it will earn 10% of the printer ink business by offering an ink cartridge refill program. If the estimate is correct, what is the probability that more than 800 of the 7500 persons who need ink will use this Walgreens program?

To determine

To calculate: The probability of more than 800 persons that uses ink from a cartridge refill program for their work if the program make profit of 10% through ink business.

Explanation

Given Information:

A cartridge refill program sells their ink at 10% profit to 7500 persons through ink business.

Formula used:

The condition for the approximated normal distribution from binomial probability distribution is,

np5 and nq5,

The theoretical mean for the distribution is given as,

μ=np

Where n is the number of independent trials and p is the probability of success.

The standard deviation for the distribution is,

σ=npq

The z- score for the standard deviation σ and theoretical mean μ is,

z=xμσ

Calculation:

The probability of success is the probability of earning printer ink business.

p=0.10

Use the formula for the compliment of probability p,

q=1p

Substitute 0.10 for p.

q=10.10=0.90

Apply the normal approximation, the value of theoretical mean np is given as,

np=7500(0.10)=750

The value of nq5 is given as,

nq=7500(0.90)=6750

Since nq5 and nq5 so the binomial distribution can be use as normal approximation distribution.

Use the formula for the theoretical mean,

μ=np

Substitute 7500 for n and 0.10 for p,

μ=7500(0.10)=750

Use the formula for the standard deviation of a binomial distribution,

σ=npq

Substitute 7500 for n, 0

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