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2 years ago

5

Jason begins at the start of a path and rides his bike 11 12 miles on the path. The path is 12 14 miles long. Enter the distance

, in miles, Jason must ride to reach the end of the path. Show your work.

1 answer:

nikitadnepr [17]2 years ago

6 0

Answer:

Number of miles remaining for Jason to reach end of the path = 3/4 miles

Step-by-step explanation:

Total distance of the path = 12 1/4 miles

Distance reached by Jason's bike on the path = 11 1/2 miles

Enter the distance, in miles, Jason must ride to reach the end of the path.

Number of miles remaining for Jason to reach end of the path = Total distance of the path - Distance reached by Jason's bike on the path

= 12 1/4 miles - 11 1/2 miles

= 49/4 - 23/2

= (49-46) / 4

= 3/4 miles

Number of miles remaining for Jason to reach end of the path = 3/4 miles

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To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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:

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In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

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$Z = \frac{11.2 - 11}{0.6}$

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$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

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b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

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$Z = \frac{11 - 11}{0.6}$

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$Z = 0$ has a pvalue of 0.5.

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$Z = \frac{10.5 - 11}{0.6}$

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This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

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$Z = -0.67$

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0.497, rounded to three decimal places.

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