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Vladimir79 [104]
3 years ago
14

Carmen ran one mile in 7 minutes. At this rate, how long will it take her to run 5 miles?

Mathematics
1 answer:
Gala2k [10]3 years ago
3 0
It would take her 35 minutes to run 5 miles
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P(X&lt; ) 1-P(X&gt; ) A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball
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Binomial probability distribution

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Normal probability distribution

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

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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

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