Exam 4: Random Variables and Probability Distributions

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 42 home runs in 800 at-bats?

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 0 2 4 6 8 p(x) -.1 .1 .2 .3 .5

Management at a home improvement store randomly selected 45 customers and observed their shopping habits. They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store.

In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable. x (x) 0 .30 1 .40 2 .20 3 .06 4 .04

Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game

Assume that $x$ is a binomial random variable with $n = 400$ and $p = 0.30$ . Use a normal approximation to find $P ( x > 110 )$ .

As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability that one of the two phones is faulty.

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 100$ and $d = 20$ . Find $P ( x \geq 100 )$ .

The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 5 goals per game. Find the probability that the team scored exactly three goals in each of four randomly selected games.

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds.

Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that during a randomly selected month PCE's were between $775.00 and $990.00?

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 8.5 to 10.5 millimeters. Any ball bearing with a diameter of Over 10.25 millimeters or under 8.75 millimeters is considered defective. What is the probability That a randomly selected ball bearing is defective?

The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 6. Find the probability that more than four road construction projects are currently taking place in the city.

The rate of return for an investment can be described by a normal distribution with and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 43.5%?

You test 4 items from a lot of 15. What is the probability that you will test no defective items if the lot contains 3 defective items?

According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that more than 22 of the women sampled have not been the victim of domestic abuse.

A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the approximate probability that more than 17 and less than 26 of the sampled students had at least one tattoo.

A literature professor decides to give a 15-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than .10. What score should be set as the lowest passing grade?

Classify the following random variable according to whether it is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic