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P(X< ) 1-P(X> ) A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball

Inessa [12570]

Answer:

The likelihood is 19.49% that no more than 16 of them are strikes

Step-by-step explanation:

Using the binomial probability distribution

The probability of a specific number of successes in n repeated trials, with a given probability p.

This can be approximated to a normal distribution, utilizing the expected value and standard deviation.

The expected value for the binomial distribution is:

$E(X) = np$

The standard deviation for the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

For normal probability distributions

Problems related to normally distributed samples can be analyzed utilizing the z-score formula.

In a dataset characterized by a mean $\mu$ and a standard deviation $\sigma$ , the z-score for a measure X can be calculated as:

$Z = \frac{X - \mu}{\sigma}$

The z-score indicates how many standard deviations a measure is from the average. After computing the z-score, one can reference the z-score table to find the associated p-value. This p-value represents the probability that the measure's value is less than X, thus indicating the percentile of X. By subtracting this p-value from 1, we derive the likelihood that the measure's value surpasses X.

When approximating a binomial distribution with a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .