TRUE or FALSE:

problem 1: Mutually exclusive events are also independent.

problem 2: If events A and B are independent, then the probability of A given B, that is, P(A|B) is generally not equal to 0.

problem 3: Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as independent events.

problem 4: In a binomial distribution the random variable X is continuous.

problem 5: The variance of the binomial distribution is √np(1-p)

problem 6: The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and the probability of success on any trial must be the same.

problem 7: The mean and variance are the same for a standard normal distribution.

problem 8: In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is discrete.

problem 9: For a discrete random variable which can take values from 0 to 150, P(X ≤ 100) is greater than P(X<100).

problem 10: The number of defective pencils in a lot of 1000 is an ex of a continuous random variable.

problem 11: All continuous random variables are normally distributed.

Multiple Choice problems:

problem 1: Two mutually exclusive events having positive probabilities are ______________ dependent.

A) Sometimes
B) Always
C) Never

problem 2: ___________________ is a measure of the chance that an uncertain event will occur.

A) Random experiment
B) Sample Space
C) Population
D) Probability
E) Probability Distribution

problem 3: In which of the following cases can we say that A₁ and A₂ are complements?
A) A₁ and A₂ are mutually exclusive
B) A₁ and A₂ are totally exhaustive
C) A₁ and A₂ are independent
D) P(A₁/A₂)= P(A₁)
E) If both A and B are satisfied

problem 4: In which of the following are the two events A₁ and A₂, independent?
A) A₁ and A₂ are mutually exclusive
B) The intersection of A₁ and A₂ is zero
C) The probability of A or B is the sum of the individual probabilities
D) P(A₁/A₂) = P(A₁)
E) Choices A and B

problem 5: If p = .45 and n= 15, then the corresponding binomial distribution is:

A) Left skewed
B) Right skewed
C) Symmetric
D) Bimodal

problem 6: Which of the following is a valid probability value for a random variable?

A) -0.7
B) 1.01
C)  0.2
D) All of the above

problem 7: Which of the following statements about the binomial distribution is not correct?

A) Each trial results in a success or failure
B) Trials are independent of each other
C) The probability of success remains constant from trial to trial
D) The experiment consists of n identical trials
E) The random variable of interest is continuous

problem 8: Which one of the following statements is an essential assumption of the binomial distribution?

A) Sampling must be done with replacement
B) The probability of success remains constant from trial to trial
C) The probability of success is equal to the probability of failure in each trial
D) The number of trials must be greater than 2
E) The total number of successes in an experiment cannot be zero

problem 9: A fair die is rolled 10 times. What is the probability that an even number (2, 4 or 6) will occurless than 3?

A) 0.0547
B) 0.1719
C) 0.8281
D) 0.1172
E) 0.9453

problem 10: In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 12 teachers who have recently left their profession. Find the probability that 5 or more of them were laid off.

A) 0.2311
B) 0.7237
C) 0.2763
D) 0.7689
E) 0.4925

problem 11: The probability or the area under the normal curve between Z = 2 and Z = 3 is ________________ the area under the normal curve between Z = 1 and Z = 2.

A) equal to
B) less than
C) greater than
D) A, B or C above dependent on the value of the mean
E) A, B or C above dependent on the value of the standard deviation

problem 12: If the normal random variable X has a mean of µ and a standard deviation σ, then (X-µ)/σ has a mean and standard deviation, respectively:

A) 1 and 0
B) X ¯and s
C) µ and σ
D) 0 and 1

problem 13: The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh more than 904 grams?

A) 0.8849
B) 0.3849
C) 0.1151
D) 0.7698
E) 0.2302