Bernoulli sequences and the binomial distribution
Continuous Random Variables
Sampling and estimation
Normal Distribution
Random Questions
100
A fair die is to be rolled 90 times. If x is the number of times a six is observed then the expected value of
X,E(X)
, is equal to:
What is 15?
100
If a random variable X has a probability density function:
the mean of X is:
What is 3.125?
100
In order to estimate the proportion of teenagers in Australia who smoke, a researcher selected a random sample of 200 teenagers and found that 25% of them smoked. This percentage is an example of a:
What is a sample statistic?
100
Pr(Z<−1.983), where Z is a standard normal random variable is closest to
What is 0.0237?
100
The area of triangle LMN, in
cm^2 is:
What is
15 sin 40^o
200
Suppose that X is the number of female children born into a family. If the distribution of X is binominal, with probability of success of 0.48, then the probability that a family with five children will have two female children is:
What is
5C2(0.48)^2(0.52)^3?
200
A random variable X has a probability density function as shown:
the value of k is:
What is 5?
200
A bag contains 4 black balls and three blue balls. If a random sample of three balls is taken from the bag, without replacement, the possible values of the sample proportion of the blue balls in the sample are:
What is 
200
If a random variable XX is normally distributed with a mean of 100 and a standard deviation of 10, then Pr(82<X<112) is closest to:
What is 0.8490?
200
Given that for f(x)=xsinx,f′(x)=sinx+xcosx, an antiderivative of xcosx is:
xsinx+cosx
300
If the proportion of batteries that are defective is 0.0030, then the standard deviation of the number of defective batteries in a sample of size 1000 is closest to (assume a binomial distribution):
What is 1.729?
300
What's green and stands in the corner?
What is a naughty frog?
300
Suppose that 12% of the people in a certain country have red hair. If a random sample of 65 people is selected from that country, the mean and standard deviation of the proportion of people with red hair in the sample are:
What is 
300
What's the difference betweena guitar and a fish?
What is you can't tuna fish?
300
What is the sport that Mr Werth ruptured his ACL in?
What is football (the reall football)?
400
Suppose the random variable X represents the number of heads recorded when a fair coin is tossed 100 times.
The mean and the variance of X are equal to
What is E(X)=50, Var (X)=25?
400
What is 0.6?
400
If a researcher increases her sample size by a factor of 9, then the width of a 95% confidence interval would:
What is decrease by a factor of 3?
400
The weight of a certain breed of cat is normally distributed with a mean of 3.3 kg and a standard deviation of 1.0. If there are 50 cats of this breed at a cat show, approximately how many would be expected to weigh more than 4 kg?
What is 12?
400
What is 
500
For a particular binomial distribution with nn independent trials, each with probability of success p, the mean and variance are 5 and
4 1/6
respectively. Which of the following gives the correct values for n and p?
What is n=30 and p=
2 xx 2/(3*x^2)1/6?
500
A teacher has determined that the bottom 20% of students will be asked to re-sit the maths test. If the distribution of scores on the test is a random variable X with a probability density function:
then the maximum score for which a student will be asked to re-sit the examination is closest to:
What is 30?
500
A survey is conducted to determine the percentage of students in Year 12 who intend to go take a gap year after they finish secondary school. In a random sample of 200 students 18% indicated this intention. Determine a 99% confidence interval for the percentage of students in Year 12 who intend to take a gap year.
What is 11.0% to 25.0%?
500
Scores on an exam are known to be normally distributed, with a standard deviation of 1010. If 9% of the people who sat for the exam scored more than 75 marks, then the mean examination score is closest to
What is 62?
500
Evaluate 
(no calculator)
What is 9?