Exam 8: Continuous Probability Distributions

If the random variable X is exponentially distributed with  = 2 parameter, then the variance of the distribution is 0.5.

Let z1 be a z-score that is unknown but identifiable by position and area. If the symmetrical area between -z1 and + z1 is 0.9544, the value of z1 is 2.0.

If the random variable X is normally distributed with a mean of 70 and a standard deviation of 10, find the following values of the distribution of X. a. First quartile. b. Third quartile.

The probability density function f(x) of a random variable X that is normally distributed is completely determined once the:

The active lifetime of laptop computers is normally distributed, with a mean of 36 months and a standard deviation of 6 months. a. What is the probability that a randomly selected laptop will last less than 3.5 years? b. What proportion of the laptops will last more than 32 months? c. What proportion of the laptops will last between 2 and 4 years?

The probability density function f(x) of a random variable X that is uniformly distributed between a and b is:

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter?

A random variable X is normally distributed with a mean of 250 and a standard deviation of 50. Given that X = 175, its corresponding z-score is -1.50.

Using the standard normal curve, the z-score representing the 75th percentile is 0.75.

If the random variable X is exponentially distributed and the parameter of the distribution  = 4, then P(X  0.25) = 0.3679.

Using the standard normal curve, the z-score representing the 90th percentile is 1.28.

The mean and standard deviation of an exponential random variable cannot equal to each other.

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if:

If Z is a standard normal random variable, find the value of z that has the following probabilities: a. $\mathrm { P } ( Z \leq z ) = 0.3228$ b. $\mathrm { P } ( Z \geq z ) = 0.8289$

Find the value of µ, if X is a normal random variable, with standard deviation 2, and 2.5% of the values are below 1?

In the normal distribution, the flatter the curve, the larger the standard deviation

Which of the following is not true for an exponential distribution with parameter $\lambda$ ?

If Z is a standard normal random variable, find the value z for which: a. the area to the left of 0.0336. b. the area to the right of z is 0.0075. c. the area to the left of z is 0.0.9909.

If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities: a. $P ( X \leq 87 )$ b. $P ( X \geq 91 )$ c. $P ( X = 78 )$

A certain brand of flood lamps has a lifetime that is normally distributed with a mean of 3750 hours and a standard deviation of 300 hours. a. What proportion of these lamps will last for more than 4000 hours? b. What lifetime should the manufacturer advertise for these lamps in order that only 2% of the lamps will burn out before the advertised lifetime?