# Probability Theory and Ans

Topics: Probability theory, Normal distribution, Binomial distribution Pages: 3 (651 words) Published: April 9, 2012
STA 2023 Test on sections 6.1, 6.2, 7.1-7.3, and 7.5

STA 2023 Test on sections 6.1, , and 6.2.

Classify the following random variable as to whether it is discrete or continuous.

1) The number of runs scored in a baseball game.
A) continuousB) discreteAns = B

2) The cost of a road map.
A) continuousB) discrete Ans = B

Provide an appropriate response.

3) A random variable is
A) generated by a random number table.
B) the variable for which an algebraic equation is solved.
C) a numerical measure of a probability experiment..Ans = C
D) a qualitative attribute of a population.

4) Given the table of probabilities for the random variable x, does this form a probability distribution? Answer yes or no.

x 5101525
P(x)0.1–0.10.30.8 Ans = No

5) True or False: The expected value of a discrete random variable may be negative Ans = True

6) The table of probabilities of the random variable x is given as:

x 0125
P(x)0.50.20.20.1

Find the mean, µ and standard deviation, σ of x. Round answers to one decimal place. Ans = µ = 1.1, σ = 1.5

7) If p is the probability of success of a binomial experiment then the probability of failure is
A) 1B) –pC) 1–pD) p + 0.5 Ans = C

8) A binomial experiment has 6 trials with the probability of success on any trial = p = 0.5. Find the probability of exactly 2 successes in the 6 trials. (Use the binomial probability distribution function.) Ans = 0.2344

9) Assume that male and female births are equally likely and the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three girls in nine births.Ans = 0.1714 exact Ans = 0.1719 normal approx

10) A test consists of 16 True False questions. If a student guesses on each question what is the mean number of correct answers?...