   Chapter 8.5, Problem 37E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# In the following problems, use a normal approximation to the binomial.Knee operations The probability is 0.025 that a knee operation at Memorial Hospital has complications that warrant reopening the knee. If the hospital performs 1300 knee operations in a year, what is the probability that 45 or more of the operations will result in complications?

To determine

To calculate: The probability that 45 or more out of 1300 knee operations would result in complications.

Explanation

Given Information:

The probability is 0.025 that a knee operation at Memorial hospital has complications that warrant reopening of knee. It is also given that 45 or more out of 1300 knee operations would result in complications.

Formula used:

For a binomial distribution,

Mean is μ=np and standard deviation is,

σ=npq

The zscore is,

z=xμσ

Where, q=1p.

Where n the number of trials, p is the probability of success, and q is the probability of failure.

Calculation:

Consider the probability that 45 or more out of 1300 knee operations would result in complications.

Then the mean is,

μ=np=1300(0.025)=32.5

And the probability of failure is q=1p.

q=10.025=0.975

And the standard deviation is,

σ=npq=1300(0

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