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Probability

The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.

14,643 Questions

Does variance and standard deviation assume nominal data?

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.

What is the difference between poisson and binomial distribution?

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.

How do you get if you roll a die 100 times how many times would you expect to get 1?

If you roll a die 100 times, you would expect to get a 1 about 17 times, because the probability of getting a 1 is 1 in 6, or 0.1667. However, that is theoretical probability; experimental probability - the actual results of doing this 100 times - might not be 17, but if you did this a large number of times, the experimental results would indeed begin to approach the theoretical results.

What is the probability if rolling a sum of 7 or 8 given the second die is a 1 or a 2?

1/4 = 0.25

If the second die is 1 or 2, then there are 12 possible outcomes.

To score 7: 5+2 or 6+1 ⇒ 2 rolls

To score 8: 6+2 ⇒ 1 roll

⇒ to score 7 or 8: 2 + 1 = 3 rolls

So there are 3 rolls to score the required sums out of 12 possible rolls, giving a probability of:

3/12 = 1/4 = 0.25

What is the difference of a normal distribution and a stardard normal distribution?

The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.

What is the probability of rolling a 7 on a regular six-sided die?

The probability of rolling a 7 on a standard die is 0. It will not ever happen.

What z-score corresponds to this value?

There is insufficient information in the question to answer it. To determine Z score, you need raw score, mean, and standard deviation. Please restate the question.

What are the outcomes for rolling a die and and tossing a coin?

The sample space for rolling a die is [1, 2, 3, 4, 5, 6] and the sample space for tossing a coin is [heads, tails].

How many ways are there to arrange the letters in ALABAMA?

There are 210. Although the number of possible combinations of any 7 elements is (7!) or 7 factorial - 7 x 6 x 5 x 4 x 3 x 2 x 1 or 5040, there is no way to distinguish the identical elements, which are the 4 A's. So the number of combinations in this spelling exercise is (7!) divided by (4!), 5040/24 = 210.

As an equation: (7!)/(4!) = (7 x 6 x 5) = 210

By Arrangement

If you looked at the A's as separators, and then calculated the number of ways that the 3 remaining letters could be fit into the 5 spaces, it would look something like this:

_A_A_A_A_

LBMA_A_A_A_

ALBMA_A_A_

A_ALBMA_A_

and so forth.

Grouped together, L B and M can be arranged in 6 distinct ways. There are

5 ways to keep the three letters together along with the separators, so that

makes 30 possibilities.

There are 20 ways to have 2 letters of the three together, with the third

someplace else. (5 different locations for a group of two, leaving four possible

locations for the remaining letter) In each of the 20 configurations the 3 letters

can still be arranged in 6 distinct ways, making 120 more possibilities.

So there are 10 different ways to keep the three letters separate from each other, and each of the 10 ways can still have the three letters in 6 different arrangements, giving 60 more possibilities.

30 + 120 + 60 = 210.

What is the z score of 6.56 and how do you find it?

There is insufficient information in the question to answer it. To determine Z-Score, you need raw score, which you gave, but you also need mean and standard deviation, which you did not give. Please restate the question.

How many permutations of the letters in the word Louisiana are there?

The number of permutations of the letters in the word LOUISIANA is 9 factorial or 362,880. However, since the letters I and A are each repeated once, you need to divide that by 4 to determine the number of distinct permutations, giving you 90,720.

What is the probability of rolling two 2's on two six-sided die?

The chance is 1/36.

(There are 36 possible combinations for two 6-sided dice, but only 18 separate combinations when the dice are not considered seperately.)

How can you simplify 31 over 36?

Well, honey, simplifying 31 over 36 is like trying to fit into your high school jeans after Thanksgiving dinner. You just divide the top and bottom by the greatest common factor, which in this case is 1. So, 31 over 36 stays as is because there's no simpler way to write it.

What role do z-scores play in the transformation of data from multiple distributions to the standard normal distribution?

None.

z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.

What is the z-score for a test score of 110?

In order to know the z-score, given a test score, you must also know the mean and the standard deviation. Please restate the question.

How many distinguishable permutations are there of the letters in the word effective?

The number of permutations of the letters EFFECTIVE is 9 factorial or 362,880. To determine the distinct permutations, you have to compensate for the three E's (divide by 4) and the two F's (divide by 2), giving you 45,360.

What is the z score of x equals 108?

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

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