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Oksi-84 [34.3K]
2 years ago
7

For how many minutes did Lynn run at a greater speed than Kael? 12 17 23 28.

Mathematics
1 answer:
Archy [21]2 years ago
4 0

Answer:

<u><em>28 minutes.</em></u>

Step-by-step explanation:

We can see from our graph that 12 minutes after starting the race Lynn left Kael behind and he ran at a greater speed till the race ended after 40 minutes.

To find total number of minutes Lynn ran faster than Kael we will subtract 12 from 40.

Therefore, Lynn ran at a greater speed than Kael for <u><em>28 minutes.</em></u>

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c) For this case we want to find a value of z that satisfy:

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And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got z_{\alpha/2}=1.64

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Part a

P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

"=NORM.INV(0.025,0,1)"

And for this case the two values are :z_{crit}= \pm 1.96

Part b

P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates \alpha/2 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

"=NORM.INV(alpha/2,0,1)"

Part c

For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got z_{\alpha/2}=1.64

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Step-by-step explanation:

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