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?

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