Exam 8: Continuous Probability Distributions

A bank has determined that the monthly balances of the saving accounts of its customers are normally distributed, with an average balance of $1200 and a standard deviation of $250. What proportions of the customers have monthly balances: a. less than $1000? b. more than $1125? c. between $950 and $1075?

Given that the random variable X is normally distributed with a mean of 20 and a standard deviation of 7, P(28 $\le$ X $\le$ 30) is:

Find the value of σ if it is know that X is normally distributed with mean 5 and 14.92% of the values are above 8?

Using the standard normal curve, the z-score representing the 10th percentile is 1.28.

The mean and the standard deviation of an exponential distribution are equal to each other.

If Z is a standard normal random variable, find the value z for which: a. P(0 $\leq$ Z $\leq$ z) = 0.276. b. P(Z $\geq$ z) = 0.341. c. P(Z $\geq$ z) = 0.819. d. P(-z $\leq$ Z $\leq$ z) = 0.785. e. P(Z $\leq$ z) = 0.9279.

What are the values of z that correspond to the P(-z $\le$ Z $\le$ z) equal to 0.4778?

In the normal distribution, the mean, median and mode are all at the same position on the horizontal axis since the distribution is symmetric.

If we standardise the normal curve, we express the original x values in terms of their number of standard deviations away from the mean.

Which of the following is true for a normal distribution?

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5. What proportions of the values of X are: a. less than 14? b. more than 8? c. between 10 and 13?

Given that Z is a standard normal random variable, the mean of Z is:

The mean of the exponential distribution equals the mean of the Poisson distribution only when the former distribution has a mean equal to:

If the random variable X is exponentially distributed with parameter $\lambda$ = 1.75, then P(1.5 $\le$ X $\le$ 3.8), up to 4 decimal places, is:

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

Let z₁ be a z-score that is unknown but identifiable by position and area. If the area to the right of z₁ is 0.7291, the value of z₁ is -0.61.

If the random variable X is exponentially distributed and the parameter of the distribution $\lambda$ = 4, then P(X $\le$ 0.25) = 0.3679.

If the continuous random variable X is uniformly distributed over the interval [15, 25], then the mean of X is:

A used car salesman in a small town states that, on the average, it takes him 5 days to sell a car. Assume that the probability distribution of the length of time between sales is exponentially distributed. a. What is the probability that he will have to wait at least 8 days before making another sale? b. What is the probability that he will have to wait between 6 and 10 days before making another sale?

If the mean of an exponential distribution is 4, then the value of the parameter $\lambda$ is: