# Question

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. Then, if X denotes the distance (in miles) of an emergency from the northernmost point of this stretch of river, its probability density function is as follows:

a. Graph the probability density function.

b. Find and graph the cumulative distribution function.

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

d. The rescue team’s base is at the midpoint of this stretch of river. Find the probability that a given emergency arises more than 1.5 miles from this base.

a. Graph the probability density function.

b. Find and graph the cumulative distribution function.

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

d. The rescue team’s base is at the midpoint of this stretch of river. Find the probability that a given emergency arises more than 1.5 miles from this base.

## Answer to relevant Questions

Delivery trucks arrive independently at the Floorstore Regional distribution center with various consumer items from the company's suppliers. The mean number of trucks arriving per hour is 20. Given that a truck has just ...A random variable X is normally distributed with a mean of 100 and a variance of 500 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation ...It is estimated that in normal highway driving, the number of miles that can be covered by automobiles of a particular model on 1 gallon of gasoline can be represented by a random variable with mean 28 and standard deviation ...The random variable X has probability density function as follows: a. Graph the probability density function for X. b. Show that the density has the properties of a proper probability density function. c. Find the ...A pizza delivery service delivers to a campus dormitory. Delivery times follow a normal distribution with a mean of 20 minutes and a standard deviation of 4 minutes. a. What is the probability that a delivery will take ...Post your question

0