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Identify the parameters [tex]p[/tex] and [tex]n[/tex] in the following binomial distribution scenario.

A softball pitcher has a 0.579 probability of throwing a strike for each pitch and a 0.421 probability of throwing a ball. If the softball pitcher throws 27 pitches, we want to know the probability that exactly 17 of them are strikes. (Consider strikes as successes in the binomial distribution.)

Select the correct answer below:

A. [tex]p=0.421, n=27[/tex]

B. [tex]p=0.421, n=17[/tex]

C. [tex]p=0.579, n=17[/tex]

D. [tex]p=0.579, n=27[/tex]



Answer :

GinnyAnswer
To solve this problem, let's carefully identify the parameters [tex]$p$[/tex] and [tex]$n$[/tex] within the context provided.

1. Determine the probability of success [tex]$p$[/tex]:
- In this scenario, a "success" is defined as the pitcher throwing a strike.
- The given probability that the pitcher throws a strike is 0.579.

2. Determine the number of trials [tex]$n$[/tex]:
- Here, the pitcher makes a total of 27 pitches.
- The number of trials [tex]$n$[/tex] is therefore 27.

Thus, based on the information provided, we conclude that:
- The probability of success ([tex]$p$[/tex]) is 0.579.
- The number of trials ([tex]$n$[/tex]) is 27.

The correct parameters are:
[tex]$p=0.579, n=27$[/tex]

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