Exam 5: Normal, Binomial, Poisson, and Exponential Distributions

The Poisson probability distribution is one of the most commonly used continuous probability distributions.

What is the probability that a randomly selected customer will spend $30 or more?

What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

The mean and standard deviation of a normally distributed random variable that has been "standardized" are zero and one, respectively.

Only 5% of the students taking the test scored higher than what value?

How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day?

The binomial random variable represents the number of successes that occur in a specific period of time.

A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance if np > 5 and n(1-p) > 5.

The local police department is interested in estimating the number of cars that fail to stop at a stop sign during a specified lunch hour. Which probability distribution should they use?​

Find P(X = 10).

What is the probability that a randomly selected customer will spend between $20 and $35?

What is the probability that between two and four (inclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?

There is a 5% chance that GM will sell more than what number of cars during the next year?

The density function specifies the probability distribution of a continuous random variable.​

Given that Z is a standard normal variable, the value z for which P(Z z) = 0.2580 is:

The Poisson random variable is a:

An exponential distribution with parameter = 0.2 has mean and standard deviation both equal to 5.

Suppose that an highway patrol officer can obtain radar readings on 500 vehicles during a typical shift. How many traffic violations would be found in a shift?

​A restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day. Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent. Why is the independence assumption in this scenario probably not realistic? Using a more realistic assumption, do you think the probability would increase or decrease?

Much of the study of probabilistic inventory models, queuing models, and reliability models relies heavily on the Poisson and exponential distributions.