Bernoulli sequences and the binomial distribution
Continuous Random Variables
Sampling and estimation
Normal Distribution
Trigonometry
Calculus
100
A fair die is to be rolled 90 times. If X represents the number of times a six is observed then the expected value of
X,E(X)
, is equal to:
What is 15?
100
A random variable X has a probability density function as shown:
the value of k is:
What is 5?
100
Explain what would happen to a confidence interval if you increased the sample size but the sample proportion and level of confidence stayed the same:
The width of the confidence interval would decrease.
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 or 9.64 cm2
100
Evaluate 
(no calculator)
What is 9?
200
Let X be the number of female children born into a family in a particular country, where the probability of a child being female is 0.48. An expression for the probability that a family with five children will have two female children is:
What is
5C2(0.48)^2(0.52)^3?
200
If a random variable X has a probability density function:
the mean of X is:
What is 3.125?
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 {0, 1/7, 2/7, 3/7}
200
If a random variable X is normally distributed with a mean of 500 and a variance of 10 000, then Pr(250<X<400) is closest to:
What is 0.1524?
200
In a triangle ABC, a=5, b=6 and C= 105^@.
The length of side c is:
What is 8.75
200
For the function,
f(x)=8x^3-x^4,
the coordinates of the global maximum are:
What is Maximum at (6, 432)?
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 is 0.6?
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
Tech Free!
The results of a state wide exam are normally distributed. If the middle 68% of entrants scored between 8 and 12 points, the approximate mean and standard deviation of the distribution are:
What is
mu=10, sigma=2.
300
The area of a triangle is 52.01 cm2. Angle A is 52 degrees, side c is 12 cm. What is the length of side b?
What is 11cm.
300
The position, x metres, of a particle travelling in a straight line from a fixed origin at time t seconds is given by x(t)=2t3-12t2+8t, t>/=0. Determine the particles initial acceleration.
What is -24 m/s2
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
X is a continuous random variable with a probability density function defined by
f(x)={(1/2x,0<=x<=2),(0, elsewhere):}
The P(X>1.5) is:
What is 0.4375
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, the approximate number expected to weigh more than 4 kg:
What is 12?
400
Tech-Free!
A block of land is known to be in the shape of an isosceles triangle. The unequal side is 4km in length and the equal angles are labelled beta where cos(beta)=sqrt(5)/3.
The exact area of this site is:
What is
(8sqrt(5))/5 km^2
400
The sum of two non-negative numbers is 30. Determine the minimum values for the sum of their squares.
What is the minimum value of the sum of their squares is 450.
500
A binomial distribution with n independent trials, each with probability of success p, the mean and variance are 5 and
4 1/6
respectively. The values for n and p are:
What is n=30 and p=
1/6?
500
Consider the continuous random variable with probability density function:
f(x) = {3/13(x2+4) 0</= x </= 1
0 otherwise
Calculate the standard deviation correct to 4 decimal places.
What is 0.2903?
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%, 25.0%)?
500
Scores on an exam are known to be normally distributed, with a standard deviation of 9.69. 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
A triangle has two sides of length 9.5cm and 13.5cm, and one angle of 40.2^@.
2 possible areas of the triangles are:
What are 58.57 and 28.09 cm2.
500
The acceleration (in m/s2) of a particle moving in a straight line is given by
(dv)/(dt)=4e^t-6t+1
where v is the velocity at any time.
If the particle starts at the origin with a velocity of -1m/s, the displacement from the origin after 1 second is:
What is
4e-19/2 metres