The length of time (in seconds) that a user views a page on a Web site before moving to another page is a lognormal random variable with parameters $\theta=0.5 \text { and } \omega^{2}=1$ (a) What is the probability that a page is viewed for more than 10 seconds? (b) What is the length of time that 50% of users view the page? (c) What is the mean and standard deviation of the time until a user moves from the page?

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes. a. What is the probability that a battery lasts more than four hours? b. What are the quartiles (the 25% and 75% values) of battery life? c. What value of life in minutes is exceeded with 95% probability?

The weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounce. a. What is the probability that a shoe weighs more than 13 ounces? b. What must the standard deviation of weight be in order for the company to state that 99.9% of its shoes weighs less than 13 ounces? c. If the standard deviation remains at 0.5 ounce, what must the mean weight be for the company to state that 99.9% of its shoes weighs less than 13 ounces?

The life (in hours) of a magnetic resonance imaging machine (MRI) is modeled by a Weibull distribution with parameters β = 2 and δ = 500 hours. Determine the following: a. Mean life of the MRI b. Variance of the life of the MRI c. Probability that the MRI fails before 250 hours

For what value(s) of the angle $\theta$ will the acceleration of the 80-lb block be 26 $ft/sec^2$ to the right? $\mu_{s}=0.6, \mu_{k}=0.5$

The life (in hours) of a computer processing unit (CPU) is modeled by a Weibull distribution with parameters β = 3 and δ = 900 hours. Determine (a) and (b): a. Mean life of the CPU b. Variance of the life of the CPU. c. What is the probability that the CPU fails before 500 hours?

A driver’s reaction time to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds. a. What is the probability that a reaction requires more than 0.5 seconds? b. What is the probability that a reaction requires between 0.4 and 0.5 seconds? c. What reaction time is exceeded 90% of the time?

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of five minutes. a. What is the probability that more than three customers arrive in 10 minutes? b. What is the probability that the time until the fifth customer arrives is less than 15 minutes?

Calls to a telephone system follow a Poisson distribution with a mean of five calls per minute. (a) What is the probability that exactly four calls occur within one minute? (b) If 10 separate one-minute intervals are chosen, what is the probability that all intervals contain more than two calls?

A communication channel is being monitored by recording the number of errors in a string of 1000 bits. Data for 20 of these strings are given here. (Read the data left to right, then down.)

$$\begin{matrix} \text{3} & \text{2} & \text{4} & \text{1} & \text{3} & \text{1} & \text{3} & \text{1} & \text{0} & \text{1}\\ \text{3} & \text{2} & \text{0} & \text{2} & \text{0} & \text{1} & \text{1} & \text{1} & \text{2} & \text{3}\\ \end{matrix}$$

(a) Construct a stem-and-leaf plot of the data. (b) Find the sample average and sample standard deviation. (c) Construct a time series plot of the data. Is there evidence that there was an increase or decrease in the number of errors in a string? Explain.

solve the given differential equation. y''−3y'−4y=3e2t

Given the graph of a one-to-one function y=f(x), explain how you would graph the inverse function $f^{-1}$.

Determine the mass moment of inertia about the x-axis of the solid spherical segment of mass m.

The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27 (http://phoenix.gov/WATER/wtrfacts.html). Water use in the summer is normally distributed with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons. a. What is the probability that a day requires more water than is stored in city reservoirs? b. What reservoir capacity is needed so that the probability that it is exceeded is 1%? c. What amount of water use is exceeded with 95% probability? d. Water is provided to approximately 1.4 million people. What is the mean daily consumption per person at which the probability that the demand exceeds the current reservoir capacity is 1%? Assume that the standard deviation of demand remains the same.