Question

The number of miles a motorcycle, X, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. If Mike starts a journey with one gallon of gasoline in the motorcycle, find the probability that, without refueling, he can travel more than 50 miles. Round your answer to four decimal places.

Answer 1

`P(X>50)=P((X-\mu)/(\sigma)>(50-\mu)/(\sigma))=P(Z>(50-44)/(5))=P(z>1.2)`

And we can find this probability using the normal standar distribution and with the complement rule we got:

`P(z>1.2)=1-P(z<1.2) =1-0.8849= 0.1151`

Explanation:

Let X the random variable that represent the number of miles a motorcycle of a population, and for this case we know the distribution for X is given by:

`X \sim N(44,5)`

Where
`\mu=44` and
`\sigma=5`

We are interested on this probability

`P(X>50)`

And we can use the z score formula given by:

`z=(x-\mu)/(\sigma)`

And using this formula we got:

`P(X>50)=P((X-\mu)/(\sigma)>(50-\mu)/(\sigma))=P(Z>(50-44)/(5))=P(z>1.2)`

And we can find this probability using the normal standar distribution and with the complement rule we got:

`P(z>1.2)=1-P(z<1.2) =1-0.8849= 0.1151`