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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 the following problems, use a normal approximation to the binomial.

Genetics If the ratio of boys born to girls born is 105 to 100, what is the probability that out of 2000 babies born in Santa Clara, 1030 will be girls?

To determine

To calculate: The probability that out of 2000 babies born in Santa Clara, 1030 will be girls.

Explanation

Given Information:

It is given that the ratio of boys born to girls born is 105 to 100, and out of n=2000 babies born in Santa Clara 1030 will be girls.

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 ratio of boys born to girls born is 105 to 100, And the total number of babies born are n=2000.

The sum of ratio number for babies born are 105+100=205 then the probability of baby born is girl is,

p=100205=0.48

Now, the mean is,

μ=np=2000(0.48)=960

And the probability of failure is q=1p.

q=10.48=0.52

And the standard deviation is,

σ=npq=2000(0.48)(0

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