Exam 7: Continuous Random Variables

The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime of the stereo component exceeds 1,000 days?

In order to approximate the binomial distribution using the normal distribution, the following condition(s) must be met if p is near 1.

For a continuous random variable x, the height of the probability curve f(x) at a particular point indicates the value of the probability for that value.

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly between 4.70 and 4.82 hours?

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of .15 ounce. Between what two values (in ounces), symmetrically distributed around the population mean, will 80 percent of the apples fall?

The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime of the stereo component is greater than or equal to 700 days?

________ theory is a methodology that attempts to determine the number of servers that strikes an optimum balance between the time customers wait for service and the cost of providing service.

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. Suppose that a temperature increase of 18° C or more is considered to be potentially dangerous to the environment. What is the probability that at any point in time, the temperature increase is potentially dangerous?

It is appropriate to use the uniform distribution to describe a continuous random variable x when

If the random variable, X, is normally distributed and has a mean of µ and a standard deviation σ, then the mean and standard deviation, respectively, of (X − µ)/σ are