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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

Mashutka [201]

Answer:

19.49% probability that no more than 16 of them are strikes

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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

In this problem, we have that:

$n = 30, p = 0.626$

So

$\mu = E(X) = np = 30*0.626 = 18.78$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*0.374} = 2.65$

What is the probability that no more than 16 of them are strikes?

Using continuity correction, this is $P(X \leq 16 + 0.5) = P(X \leq 16.5)$ , which is the pvalue of Z when X = 16.5. So

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

$Z = \frac{16.5 - 18.78}{2.65}$

$Z = -0.86$

$Z = -0.86$ has a pvalue of 0.1949

19.49% probability that no more than 16 of them are strikes

7 0

3 years ago

9+X+3X-5 simplify expression

Lelu [443]

4 + 4X is the expression simplified

3 0

4 years ago

Which direction does the decimal point move in when you divide by powers of 10 greater than 0?

4vir4ik [10]

Answer:

the left side is the answer

7 0

2 years ago

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PLEASE HELPP MEEE!!!!!

ale4655 [162]

Answer:

a little bit of a very nice and smart and k liye kuch bhi nahi ha ha bol rahe hai

7 0

3 years ago

Subtract 8-4 1/2. A. 3 B. 4 C. 4 1/2 D. 3 1/2

Leokris [45]

1.
An expression of the form $a \frac{b}{c}$ is called a "compound fraction"

Compound fractions can be written as simple fractions by multiplying c to a, and then adding the product to c as follows:

$a \frac{b}{c}= \frac{c.a+b}{c}$

for example,

$4\frac{1}{2}$ can be written as:

$4\frac{1}{2}= \frac{2.4+1}{2}=\frac{9}{2}$

2.

when we subtract or add a fraction $\frac{m}{n}$ from an integer k,

we first write k as a fraction with denominator n. We can do this as follows:

$k=k. \frac{n}{n}= \frac{kn}{n}$

for example, if we want to subtract $\frac{9}{2}$ from 8,

we first write 8 as a fraction with denominator 2:

$8=8. \frac{2}{2}= \frac{8.2}{2}= \frac{16}{2}$

3.

Thus,

$8-4 \frac{1}{2}= \frac{16}{2}- \frac{9}{2}= \frac{16-9}{2}= \frac{7}{2}$

4.

The simple fraction 7/2 is not an option, so we write it as a compound fraction as follows:

$\frac{7}{2}= \frac{6+1}{2}= \frac{6}{2}+ \frac{1}{2}=3+ \frac{1}{2}=3\frac{1}{2}$

(So write 7 as the sum of the largest multiple of 2, smaller than 7 + what is left. In our case these numbers are 6 and 1, then proceed as shown)

5. Answer: D

3 0

3 years ago

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