A baseball player is known to get onto 1st base 30 of the t

\" A baseball player is known to get onto 1st base 30% of the times he is at bat. That player bats 70 times.

For the binomomial experiment described above:

A. Identify n and P ( be sure to label which is which)

B. Find the mean (or expected value) for the experiment

C. Find the standard deviation for the experiment.

D. Find the probability that the player will get onto 1st base 25 or more times in his 70 at-bats.

Solution

A. Identify n and P ( be sure to label which is which)

n=70

p=0.3

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B. Find the mean (or expected value) for the experiment

mean=n*p=70*0.3 =21

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C. Find the standard deviation for the experiment.

standard deviation = sqrt(n*p*(1-p))

=sqrt(70*0.3*0.7)

=3.834058

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D. Find the probability that the player will get onto 1st base 25 or more times in his 70 at-bats.

P(X=x)=70Cx*(0.3^x)*(0.7^(70-x)) for x=0,1,2,..,70

P(X>=25)=1-P(X=0)-P(X=1)-...-P(X=24)

=1-70C0*(0.3^0)*(0.7^(70-0)) -...-70C24*(0.3^24)*(0.7^(70-24))

=0.1798504