Question

1 pts

Question 5
The size of gasoline tanks in cars is normally distributed with a mean size of 24.8 gallons and a standard
deviation of 6.2 gallons. What percent of tanks are less than 31 gallons. Round answer to the nearest
percent
84%
71%
16%
20%

Answer 1

`P(X<31)=P((X-\mu)/(\sigma)<(31-\mu)/(\sigma))=P(Z<(31-24.8)/(6.2))=P(z<1)`

And we can find this probability using the normal standard distribution or excel and we got:

`P(z<1)= 0.84`

And if we convert this into % we got 84% so then the best solution would be:

84%

Explanation:

Let X the random variable that represent the size of gasoline tanks of a population, and for this case we know the distribution for X is given by:

`X \sim N(24.8,6.2)`

Where
`\mu=24.8` and
`\sigma=6.2`

We are interested on this probability

`P(X<31)`

And we can use the z score formula given by:

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

Using the last formula we got:

`P(X<31)=P((X-\mu)/(\sigma)<(31-\mu)/(\sigma))=P(Z<(31-24.8)/(6.2))=P(z<1)`

And we can find this probability using the normal standard distribution or excel and we got:

`P(z<1)= 0.84`

And if we convert this into % we got 84% so then the best solution would be:

84%