The jurisdiction of a rescue team includes emergencies occurring on a stretch of river that is 4 miles long. Experience has shown that the distance along this stretch, measured in miles from its northernmost point, at which an emergency occurs can be represented by a uniformly distributed random variable over the range 0 to 4 miles

A. Find the probability density function

B. Find the mean and standard deviation

C. Find the probability that a given emergency arises within 1 mile of theuttermost point of this stretch of river

D. Find the probability that a given emergency arises more than 2 mile of theuttermost point of this stretch of river.

2. It is known that amounts of money spent on clothing in a year by students on a particular campus follow a normal distribution with a mean of $380 and a standard deviation of $50.

A. What is the probability that a randomly chosen student will spend less than $400 on clothing in a year?

B. What is the probability that a randomly chosen student will spend more than $360 on clothing in a year?

C. What is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?

3. The mean selling price of senior condominiums in Green Valley over a year was $215,000. The population standard deviation was $25,000. A random sample of 100 new unit sales was obtained.

A. What is the sample mean?

B. What is the standard deviation/standard error of the sample mean?

C. What is the probability that the sample mean selling price was more than $210,000?

D. What is the probability that the sample mean selling price was between $213,000 and $217,000?

E. What is the probability that the sample mean selling price is less than $220,000?

4. An administrator for a large group of hospitals believes that of all patients 30% will generate bills that become at least 2 months overdue. A random sample of 200 patients is taken.

A. What is the standard error of the sample proportion that will generate bills that become at least 2 months overdue?

B. What is the probability that the sample proportion is less than 0.25?

C. What is the probability that the sample proportion is more than 0.33?

D. What is the probability that the sample proportion is between 0.27 and 0.33?