Probability and Statistics Hw NEEDS COMPLETE BY 11:30

Test 3 MATH224 – Type I November 06, 2013

Section: Name: No credit without showing work.

1. (20 points) The number of stops at gas station or rest area while driving from Greensboro to Washington D.C. is a random variable X with the following distribution:

	0	1	2	3
		0.55	0.20	0.05

1. Fill in the blank cell in the table in order to make the probability distribution.

1. Find the probability that a person has at least two stops.

1. Find the expected value and the standard deviation of .

1. (10 points) Find all Bernoulli (or binomial) experiments in the following?

1. Surveying a group of 2000 people to ask whether or not they support health care reform

1. Counting the number of daily car accidents in Greensboro

1. Rolling a die 500 times to identify whether the outcome of each trial is an even number or an odd number

1. Surveying a group of 2000 students for their current major

1. Smartphones coming off an assembly line are inspected as defective, non-defective, or undecided

1. (20 points) A survey shows that 61% of Americans support same-sex marriage. Suppose that 7 Americans are randomly selected and asked about their opinion on same-sex marriage. Let a discrete random variable be the number of people who support same-sex marriage.

1. Find the probability that exactly three people support same-sex marriage.

1. Find the probability that the at least one American supports same-sex marriage.

1. Find the expected value and the standard deviation of .

1. (15 points) Determine whether the statement is true or false under the assumption that .

1.

1.

1.

1.

1.

1. (5 points) Assuming that , match the same probabilities between and .

0. (i)

0. (ii)

0. (iii)

1. (5 points) Assuming that , one of the values of , and in the following examples is different from the others. Which one is different?

1. .

1. .

1. .

1. .

1. (25 points) A random variable, , is known as normally distributed with and .

1. Which of the following variables is appropriate for this random variable ? (i) Human body temperature (ii) Room temperature (iii) SAT score (iv) House price

1. Find the -score for the value of 96.6. Give answer to the second decimal place.

1. Find the probability that is less than 96.6. Give answer to the fourth decimal place.

1. Find the probability that is between 97.90 and 99.36. Give answer to the fourth decimal place.

Find the 50th percentile value of this random variable. Give answer to the second decimal place.