7.Large reservoirs of oil found underground are under very high pressure, which allows the oil to be pumped to the surface. All oil fields contain some water, and as water is pumped back into a well in order to maintain high pressure, the water content increases. Suppose the proportion of water in a randomly selected barrel of oil pumped to the surface has a normal distribution with mean 0.12 and standard deviation 0.025.

Give your answer to four decimal places.

The probability that a randomly selected barrel of oil has a proportion of water between 0.15 and 0.17 is ___.

8.Economics and Finance. San Francisco is one of the most expensive cities in which to live in the United States. As of February 2013, the mean rent for a one-bedroom apartment in the Mission District was $2600 . Assume that the distribution of rents is approximately normal and the standard deviation is $200 . A one-bedroom apartment in the Mission District is selected at random.

(a) Find the probability ( 0.0001) that the rent is less than $2450 .

P(X<2450)=

(b) Find the probability ( 0.0001)that the rent is between $2560 and $2670 .

P(2560X2670) =

(c) Find a rent rr ( 0.01) such that 90 % of all rents are less than rr dollars per month.

r =

10.Economics and Finance. Some of the variables that affect the monthly payment of a new-car loan are the total amount borrowed, the interest rate, and the length of the loan. During the fourth quarter of 2012, the mean length of a new-car loan was 65 months, a record high according to Experian.

Suppose the length of a new-car loan is approximately normal with standard deviation nine months.

(a) What is the probability ( 0.0001) that a new-car loan is for at most 52 months?

P(X52) =

(b) What is the probability ( 0.0001) that a new-car loan length is between 55 and 70 months?

P(55X70) =

(c) Find a symmetrical interval ( 0.0001) about the mean such that 95% of all new-car loan lengths fall in this interval.

Interval : ( , )

(d) Suppose the amount borrowed on a new-car loan is also approximately normal with mean $20000 and standard deviation $5000 . If the length of the loan and the amount borrowed are independent, what is the probability ( 0.0001) that the loan will be for more than $26000 and for less than 60 months?

P =