A baseball player has a batting average of 0.332. Would it be unusual if he hits 22 of his next 90 at bats?

Answer 1

Hi Lidi, you'll have to use the binomial distribution to solve this. You'll also these 5 items.

Sample Size: 90

Probability of a Hit: 0.332

Mean: Sample Size * Prob (H) or 90 * 0.332 or 29.88

Variance: Mean * (1 - Prob(H)) or 29.88 * 0.668 or 19.96

Standard Deviation: Square Root of the Variance or Square Root of 19.96 or 4.47

Now that you have those, you can find the probability of getting exactly 22 hits in 90 at bats.

You can use Microsoft Excel to solve this:

In Excel (the easier way to me at least), you can use the Binom.Dist formula as follows:

=Binom.Dist(No. of Hits, Sample Size, Probability of a Hit, False) or

=Binom.Dist(22,90,0.332,False)

The final answer, using 5% as the "usual/unusual" threshold, is that getting exactly 22 hits in 90 at bats is unusual. The probability of this happening is less than 5% - it is 1.9%.

I hope this helps!

-DRP