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.  

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

believe it or not anna is correct good job anna give me a fist bump there u go gal