Answer :
Final answer:
A statistics practitioner would categorize this problem as a binomial distribution. You'd calculate the cumulative probability of 0-14 hitters being 'out'. While possible to calculate manually, statistical software is typically used for these calculations.
Explanation:
A statistics practitioner would approach this problem by identifying it as a problem of a binomial distribution. In a binomial distribution, we identify two discrete outcomes. In this case, it's either the hitter will be 'out' (with a probability of 0.80) or 'safe' on any given ground ball. We're asked to find the probability of less than 15 hitters being out, so we need to find the cumulative probability from 0 to 14 hitters being out.
The formula for the probability for a binomial distribution is:
P(X=k) = nCk * (p^k) * ((1-p)^(n-k))
Where:
n = number of trials (in this case, 20 ground balls)
k = number of 'successes' (in this case, number of hitters out)
p = probability of a 'success' (in this case, 0.80)
nCk = number of combinations of n things taken k at a time.
You would calculate this probability for k from 0 to 14, and then sum up those probabilities. While it's possible to calculate this by hand, a statistics practitioner will likely use statistical software (like Excel, SPSS, R, etc.) to do this calculation quickly.
Learn more about Binomial Distribution here:
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