Exam 11: Probability and Calculus

Given a normal distribution with mean 40 and standard deviation 8, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. -50

Given a normal distribution with mean -10 and standard deviation 5, find the area under the normal curve and above the given interval on the horizontal axis. -(-∞ , -5]

Find the median for f(x). - e

Given a normal distribution with mean 150 and standard deviation 25, find the indicated probability. -

Find a constant k so that kf is a probability density function, or state it does not exist. -

Solve the problem. -Computer experts warn that writable compact disks such as CD-Rs (Compact Disc-Recordable) and CD-RWs (Compact Disc-ReWriteable) have much shorter lifespans than other digital storage methods such as hard drives or magnetic tape. The time until the disc becomes unreadable for a particular brand of CD-RWs is a continuous random variable with probability density function given by the following function. Round to two decimal places. (A) What is the probability that a disc is not readable after 25 years? (B) What is the probability that the disc is readable after 10 years? (C) If the user wants the probability that the disc is readable to be 0.9, when is the last time it should be read?

Graph y = f(x) and find the value of -

Solve the problem. -

Find F(b), use a graphing calculator to graph F and use the graph to estimate -

Given a normal distribution with mean 40 and standard deviation 8, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. -24

Use a graphing calculator to approximate the median of the indicated probability density function f. Round to two decimal places. -

Graph y = f(x) and find the value of -

Solve the problem. -Find the area under the standard normal curve from 0 to the indicated value of z. 0.85

Find the associated cumulative distribution function. Graph both functions (on separate sets of axes). -

Solve the problem. -Use the given function to find the indicated probabilities. Illustrate each probability with a graph.

Solve the problem. -Find and graph the cumulative distribution function associated with the function.

Solve the problem. -Use the given function to find the indicated probabilities. Illustrate each probability with a graph.

Find the associated cumulative distribution function. Graph both functions (on separate sets of axes). -

Solve the problem. -The perpetual annual rent for a property is $35,000. Find the capital value at 4% compounded continuously.

Find the probability density function f and the associated cumulative distribution function F for the continuous random variable X if -X is an exponential random variable with