Question

professional tennis player serena williams has a career win record of 81%. if we took a simple random sample of 55 of her matches, what is the probability that at least 45 would be wins?

Answer 1

The probability that at least 45 would be wins is given as 43.64%

How to solve for the probability

We have to find the proportion

p  = x / n

where x = 45 wins

n = number = 55 matches

p = 45 / 55

= 0.8182

We are to find the probability of P ≥ 0.8182

The formula is given by p-µ)/σ

where

p = 0.8182

µ = 81 percent

σ = standard deviation

To get the standard deviation

√0.81(1 - 0.81) / 55

= 5.29%

We have to enter the values in the formula, such that

0.8182 - 0.81 /  0.0529

= 0.16

Using the excel formula we are to find 1 - P(Z < 0.16)

=NORM.S.DIST(z,1)

1 - 0.5636

=  0.4364

= 43.64%

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