Exam 8: Continuous Probability Distributions

Let X be a binomial random variable with n = 100 and p = 0.7. Approximate the following probabilities, using the normal distribution. a. P(X = 75). b. P(X $\le$ 70). c. P(X $\ge$ 60).

The function f(x) that defines the probability distribution of a continuous random variable X is a:

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 expected value, E(X), of a uniform random variable X defined over the interval $a \leq x \leq b$ , is:

The lifetime of a light bulb is exponentially distributed with $\lambda$ = 0.001. a. What are the mean and standard deviation of the light bulb's lifetime? b. Find the probability that a light bulb will last between 110 and 150 hours. c. Find the probability that a light bulb will last for more than 125 hours.

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.1949?

Given that z is a standard normal random variable, a negative value of z indicates that the standard deviation of z is negative.

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

Which of the following distributions is not symmetrical?

Like the normal distribution, the exponential density function f(x):

In a shopping centre, the waiting time for an elevator is found to be uniformly distributed between 1 and 5 minutes. a. What is the probability density function for this uniform distribution? b. What is the probability of waiting no more than 3 minutes? c. What is the probability that the elevator arrives in the first 30 seconds? d. What is the probability of a waiting time between 2 and 3 minutes? e. What is the expected waiting time?

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

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X?

The publisher of a daily newspaper claims that 90% of its subscribers are under the age of 30. Suppose that a sample of 300 subscribers is selected at random. Assuming the claim is correct, approximate the probability of finding at least 240 subscribers in the sample under the age of 30.

Given that Z is a standard normal random variable, P(Z > − 2.68) is:

If Z is a standard normal random variable, the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50?

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?