## Mopeds (small motorcycles) are very popular in Europe because of their mobility, ease of operation, and low cost. An article2 described a ro

Question

Mopeds (small motorcycles) are very popular in Europe because of their mobility, ease of operation, and low cost. An article2 described a rolling bench test for determining maximum vehicle speed. A normal distribution with mean value 46.8 km/h and standard deviation 1.75 km/h is postulated. Consider randomly selecting a single such moped.

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2021-11-10T01:12:45+00:00
2021-11-10T01:12:45+00:00 1 Answer
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## Answers ( )

Answer:a)

And we can find this probability using the normal standard table:

b)

And we can find this probability using the normal standard table and the complement ruel:

c)

And we can find this probability with this difference:

And in order to find these probabilities we can use the tables for the normal standard distribution, excel or a calculator.

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-scoreis “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”.Assuming the following questions:

Part a: What is the probability that the maximum speed is at most 50 km/h?Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the normal standard table:

Part b: What is the probability that maximum speed is at least 48 km/h?And we can find this probability using the normal standard table and the complement ruel:

Part c:What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?And we can find this probability with this difference:

And in order to find these probabilities we can use the tables for the normal standard distribution, excel or a calculator.