Exam 11: Probability and Calculus

Solve the problem. -Popular online video games often struggle to meet the initially high demand for access to the game servers. It is costly to increase server capacity and the demand always falls after a few months, but if the wait times are too long the game could lose sales as a result of negative criticism. The time (in minutes) a customer must wait to get into the game is a continuous random variable with probability density function given by the following function. Round to two decimal places. (A) Evaluate dx and interpret the results. (B) What is the probability that a customer waits less than 7 minutes? (C) What is the probability that a customer waits more than 10 minutes?

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

Solve the problem. -The time (in minutes) applicants must wait to receive a driver's examination is uniformly distributed on the interval [0, 80]. What is the probability that an applicant must wait more than 30 minutes?

Solve the problem. -The life expectancy (in minutes) of a certain microscopic organism 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 an organism lives for at least 10 minutes? (B) What is the probability that an organism lives for at most 8 minutes?

The quartile points for a probability density function are the values that divide the area under the graph of the function into four equal parts. Find the quartile points for the probability density function f(x). -

Solve the problem. -The length of time for telephone conversations (in minutes) is exponentially distributed. The average (mean) length of a conversation is 5 minutes. What is the probability that a conversation lasts less than 3 minutes?

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

Solve the problem. -

F(x) is the cumulative distribution function for a continuous random variable X. Find the probability density function f(x) associated with F(x). -

Find the mean, median, and standard deviation of the continuous random variable X if -X is uniformly distributed on [4, 8].

X is a continuous random variable with mean and then find ) if -X is an exponential random variable with λ = 4.

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

Solve the problem. -When a person takes a drug, the body does not assimilate all of the drug. One way to determine the amount of the drug assimilated is to measure the rate at which the drug is eliminated from the body. If the rate of Elimination of the drug (in milliliters per minute) is given by where t is the time in Minutes since the drug was administered, how much of the drug is eliminated from the body?

Solve the problem. -A building contractor's profit (in thousands of dollars) on each unit in a subdivision is a continuous random variable with probability density function f(x) as shown below. (A) Find the contractor's expected profit. Round to the nearest dollar. (B) Find the median profit. Round to the nearest dollar.

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

X is a continuous random variable with mean µ and standard deviation σ. Find µ and σ, and then find P(µ -σ ≤ X ≤ µ +σ) if -X is an exponential random variable with m = 2 ln 2.

Solve the problem. -The life expectancy of a car battery is normally distributed. The average (mean) lifetime is 235 weeks with a standard deviation of 15 weeks. If the company guarantees the battery for 4 years, what percentage of the Batteries sold would be expected to be returned before the end of the warranty period?

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

Find the value of the improper integral that converges. -

Solve the problem. -A trust fund produces a perpetual stream of income with rate flow Find the capital value at 5% compounded continuously.