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.

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-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".  

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.  

2.56 is the width of the garden

step-by-step explanation: