Probability

First, you add all the numbers together- 5+6+4=15. So the number of red marbles (5) and the total number of marbles (15)= 5/15=1/3

Yes. It will increase the standard deviation. You are increasing the number of events that are further away from the mean, and the standard deviation is a measure of how far away the events are from the mean.

Six.

I learned it in 4th grade.

A larger random sample will always give a better estimate of a population parameter than a smaller random sample.

The probability distribution is

P(X = 1) = 1/36

P(X = 2) = 3/36

P(X = 3) = 5/36

P(X = 4) = 7/36

P(X = 5) = 9/36

P(X = 6) = 11/36

P = 0 otherwise.

Mean(X) = 4.4722

Variance = 1.9715

The answer depends on what the standard deviation is.

Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution.

Binomial is the most preliminary distribution to encounter probability and statistical problems.

On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.

Neither. Its a 50:50 probability. In the long run, heads will match tails.

Sampling distribution is the probability distribution of a given sample statistic.

For example, the sample mean. We could take many samples of size k and look at the mean of each of those. The means would form a distribution and that distribution has a mean, a variance and standard deviation.

Now the population only has one mean, so we can't do this.

Population distribution can refer to how some quality of the population is distributed among the population.

There are 26*25*24*23*22 = 7,893,600 sets of initials.

The are 36 permutations of two dice. Of these, 6 permutations have the two dice with the same number, specifically 1+1, 2+2, 3+3, 4+4, 5+5, and 6+6. The probability, then, that two dice rolled will not have the same number is 30 in 36, or 5 in 6, or about 0.8333.

Oh, dude, let me break it down for you. So, if you have 17 girls and 10 boys in the class, the probability of selecting a girl is like the number of girls divided by the total number of students. So, it's 17 girls out of 27 students, which simplifies to about 63%. Cool, right?

There are 36 permutations of two dice. Of them, 6 have a sum of 7, (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1) and 2 have a sum of 11 (5+6 and 6+5). The probability, then of getting a sum of 7 or 11 is (6 plus 2) in 36, or 8 in 36, or 2 in 9, or about 0.2222.

There are 26 = 64 possible outcomes.

5 out of 36

Try to understand the subject. If in doubt ask someone to explain. Study the topics and try out plenty of past examination papers.

If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.

Yes

No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.

You need the mean and standard deviation in order to calculate the z-score. Neither are given.

It is (124 - 100)/8 = 24/8 = 3

Range can include outliers that are not normal values and can skew overall data. Most relevant values can be found within one or two standard deviations on a normal curve.

6 possible numbers to land on the first time, 6 possible numbers to land on the second time, 6x6=36