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.

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

Step-by-step 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:

Where and

We are interested on this probability

And we can use the z score formula given by:

And using this formula we got:

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

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol