Consider the following CDF for the continuous random variable X:

What is ?

Some dental insurance policies cover the insurer only up to a certain amount, say, M. (This seems to us to be a dumb type of insurance policy because most people should want to protect themselves against large losses.) Say dental expense X is a random variable with pdf:

, 

Find M so that: P(X < M) = 0.08. Present your result with two decimal values. 

Assume that the standard deviation of monthly rents paid by students in a particular town is 40 euros. A random sample of 100 students was taken to estimate the mean monthly rent paid by the whole student population.

What is the probability that the sample mean exceeds the population mean by more than 5 euros?

A normal distribution can be positively skewed.

Consider the random variable X such that .

What is F(18)? Present your result with one decimal place.

A study of hedge fund investors found that their annual household incomes are normally distributed with a mean of $175,000 and a standard deviation of $25,000. The percent of hedge fund investors that have incomes greater than $225,000 is closest to:

Consider the random variable X such that .

What is F(-1)? Present your result with two decimal places.

Tina's score on her midterm exam was at the 50th percentile. The grades were normally distributed. The exam average was 78 and the standard deviation was 6. What was Tina's score on the exam?