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Maksim231197 [3]
3 years ago
15

Major league baseball game durations are normally distributed with a mean of 160 minutes and a standard deviation of 50 minutes.

What is the probability of a game duration of between 180 and 210 minutes? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Mathematics
1 answer:
Akimi4 [234]3 years ago
4 0

Answer:

0.19

Step-by-step explanation:

μ = 160 and σ = 50.  Find the z scores for 180 and 210.

z = (x - μ) / σ

z = (180 - 160) / 50 = 0.40

z = (210 - 160) / 50 = 1.00

So we want P(0.40<z<1.00).  This can be found as:

P(0.40<z<1.00) = P(z<1.00) - P(z<0.40)

Now use a calculator or table to find each probability:

P(0.40<z<1.00) = 0.8413 - 0.6554

P(0.40<z<1.00) = 0.1859

Rounded to the nearest hundredth, P ≈ 0.19.

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Step-by-step explanation:

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So 2^{\frac{1}{2}} can be written in radical form as \sqrt{2}

So 2^{\frac{1}{2}} will be equivalent to \sqrt{2} in radical form

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