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

Answer:

$P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-\mu}{\sigma})=P(Z>\frac{50-44}{5})=P(z>1.2)$

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

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

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:

$X \sim N(44,5)$  

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:

$z=\frac{x-\mu}{\sigma}$

And using this formula we got:

$P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-\mu}{\sigma})=P(Z>\frac{50-44}{5})=P(z>1.2)$

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

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