Exam 8: Continuous Probability Distributions

If the random variable X is uniformly distributed over the interval 10 $\leq$ x $\leq$ 50, find the following probabilities. a. P(X $\geq$ 30). b. P(X $\leq$ 25). c. P(18 $\leq$ X $\leq$ 35). d. P(X = 40).

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

The values of z_A are the 100(1 - A)th percentiles of a standard normal random variable.

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as:

Consider a binomial random variable X with n = 300 and p = 0.02. Approximate the values of the following probabilities. a. P(X = 4). b. P(X $\ge$ 5). c. P(X $\le$ 8).

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

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 90th percentile is 1.28.

If the z-value for a given value x of the random variable X is z = 2.326, and the distribution of X is normal with a mean of 50 and a standard deviation of 5, to what x-value does this z-value correspond?

Using the standard normal curve, the area between z = 0 and z = 3.50 is about 0.50.

Continuous probability distributions describe probabilities associated with random variables that are able to assume any of an infinite number of values.

A continuous random variable X has the probability density function f(x) = 2 $e ^ { - 2 x }$ , x $\ge$ 0. a. Find the mean and standard deviation of X. b. What is the probability that X is between 1 and 3? c. What is the probability that X is at most 2?

Which of the following is a characteristic of a normal distribution?

The probability density function, f(x), for any continuous random variable X, represents:

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.

A continuous probability distribution represents a random variable having an infinite number of outcomes that may assume any number of values within an interval.

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

Given that X is a binomial random variable, the binomial probability P(X $\le$ x) is approximated by the area under a normal curve to the left of:

A standard normal distribution is a normal distribution with:

Which of the following is always true for all probability density functions of continuous random variables?