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Give the numerical value of the parameter p in the following binomial distribution scenarioA softball pitcher has a 0.721 probability of throwing a strike for each pitch and a 0.279 probability of throwing a ball. If the softball pitcher throws 19 pitches, we want to know the probability that more than 15 of them are strikes.

Answers

Answer 1

Answer:

Answer:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19)$

$P(X=16)=(19C16)(0.721)^(16) (1-0.721)^(19-16)=0.112$

$P(X=17)=(19C17)(0.721)^(17) (1-0.721)^(19-17)=0.051$

$P(X=18)=(19C18)(0.721)^(18) (1-0.721)^(19-18)=0.015$

$P(X=19)=(19C19)(0.721)^(19) (1-0.721)^(19-19)=0.002$

And replacing we got:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19) =0.112+0.051+0.015+0.002= 0.1801$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

Solution to the problem

For this case our random variable is given by:

$X \sim Binom(n = 19, p = 0.721)$

For this case we want this probability:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19)$

$P(X=16)=(19C16)(0.721)^(16) (1-0.721)^(19-16)=0.112$

$P(X=17)=(19C17)(0.721)^(17) (1-0.721)^(19-17)=0.051$

$P(X=18)=(19C18)(0.721)^(18) (1-0.721)^(19-18)=0.015$

$P(X=19)=(19C19)(0.721)^(19) (1-0.721)^(19-19)=0.002$

And replacing we got:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19) =0.112+0.051+0.015+0.002= 0.1801$

$P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668$

Answer 2

Answer:

Final answer:

In this binomial distribution scenario, the parameter 'p', representing the probability of success on each trial, is the probability of the pitcher throwing a strike, which is 0.721.

Explanation:

In the binomial distribution scenario you described, the softball pitcher throwing a pitch is the independent trial with two possible outcomes: throwing a strike (success) or a ball (failure). The parameter p represents the probability of success on each independent trial. From the question, we can see that the probability, or p, of the pitcher throwing a strike (success) is 0.721. Therefore, p = 0.721.

Please note that the binomial distribution model can be used when all trials are independent, the outcome of a trial is success or failure, and the probability of success remains the same for each trial. It doesn't appear that we need the number 'n' of independent trials or the random variable 'X' representing the number of successes (strikes in this case) for your question, as we were only asked for the value of 'p'.

Learn more about Binomial Distribution here:

brainly.com/question/33656163

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Answers

Answer:

(7/9) ÷ (5/4) = 28/45

Step-by-step explanation:

Fractions can be divided by using the rule "invert and multiply". We can look at the factors of 28 and 45 to see what might have been multiplied to get these numbers.

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HELP it’s not 20.40 which is what someone else answered lol

Answers

Answer:

I think it 19.6

Step-by-step explanation:

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What is the image of 2,-1 after a reflection over the y axis

Answers

The image of the point after a reflection over the y-axis is (-2, -1)

Calculating the image of the point after a reflection over the y-axis?

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Transformation rule

A reflection over the y-axis

The rule of a reflection over the y-axis is

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Answers

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Answers

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Answers

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