Probability

If a random variable X has a Normal distribution with mean m and standard deviation s, then

z = (X - m)/s

has a Standard Normal distribution. That is, Z has a Normal distribution with mean 0 and standard deviation 1.

Probabilities for a general Normal distribution are extremely difficult to obtain but values for the Standard Normal have been calculated numerically and are widely tabulated. The z-transformation is, therefore, used to evaluate probabilities for Normally distributed random variables.

A cube, by definition, must be 6 sided.

The probability of getting a 6, if it is a fair die, is 1/6.

0.0668 or about 1/15

yes

z = ±0.44

The answer depends on the distribution under consideration.

The probability of each coin flip, independently, is 0.5 or 50%. The probability of getting one result (either heads or tails) four times in a row is 0.5 to the fourth power or 0.0625, which equals 6.25%

It is 3/1024 = 0.00293, approx.

There is insufficient information in the question to properly answer it. You did not provide the list of "the following". Please restate the question.

However, by definition of probability, a probability less than 0 (the event will never happen) or greater than 1 (the event will always happen) is impossible, so maybe that answers your question.

1

Usually, it takes 2-5 flips until a head appears.

The value is 0.3055

There are 120 ways to order a 5 letter word, however, since there are two "e" letters in the word "green", the number of combinations is only 60.

yes

var(X) = (xm/a - 1)2 a/a-2 .

If a < or equal to 2, the variance does not exist.

If any numbers come up more often than any others over the long run,

then the dice are loaded and the game is not honest.

* * * * *

That is true for the roll of a die, but not dice. With 2 dice, the probabilities of the numbers are as follows

2 or 12 : 1/36 each

3 or 11 : 2/36 or 1/18 each

4 or 10 : 3/36 or 1/12 each

5 or 9 : 4/36 or 1/9 each

6 or 8 : 5/36 each

7 : 6/36 or 1/6

So 7 is the most rolled number in the long run when 2 dice are rolled.

If the population is not evenly dispersed then the sample may unfortunately come from a section that is not typical of the population. That means the sample will not be representative of the population and so any estimates for the population, based on sample statistics are biased and therefore unreliable.

For which measure of central tendency will the sum of the deviations always be zero?

Whether or not the student passes depends on the level of the examinations, the effort put in by the student, the quality of his teachers. There are too many contributory factors for a simple answer.

It is 1. Every month contains 28 days.

In 1,307,674,368,000, or 15! ways.

A discrete random variable is a variable that can only take some selected values. The values that it can take may be infinite in number (eg the counting numbers), but unlike a continuous random variable, it cannot take any value in between valid results.

Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.

Two.