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

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}

200

If a random variable X 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

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 and the domain for which f(x) is concave up are:

Maximum at (6, 432)

Concave up for 0<=x<=4

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 equation 2sin(2theta)=1.56 over the domain 0<=theta<=pi/2, has solution(s):

What is 0.273^{c} or 1.297^{c}.

300

Given that for f(x)=xsinx,f′(x)=sinx+xcosx, an antiderivative of xcosx is:

xsinx+cosx

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):}

F(x), the cumulative distribution function for f(x) is:

What is

F(x)={(0, x<0),(x^2/4, 0<=x<=2),(1, x>2):}

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 areas of this site is:

What is

(8sqrt(5))/5 km^2

400

What is

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

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 29.5?

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^@.

The area of the possible triangles are:

What are 41.39, 59.12, 61.41 and 28.41 cm^{2}.

500

The acceleration (in m/s^{2}) 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

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