Question

In: Statistics and Probability

1. Rolling dice would produce what type of distribution? 2. Outliers have the largest effect on...

1. Rolling dice would produce what type of distribution?

2. Outliers have the largest effect on which measure of central tendency?

3.Consider the following data set: 5, 10, 24, 79, 103 . If you were told to determine the mean which formula is most appropriate to use? What other formula could you use, although it is less desirable? What would you have to keep in mind if you used this second formula?

4. The mean of 10 numbers is 8. If an 11th number is now included in the results, the mean becomes 9. What is the value of the 11th number? Produce an algebraic solution. Guess and check is unacceptable.

5. Construct your own example that demonstrates why measures of central tendency can be misleading and thus measures of the variability of data are important.

Expert Solution

1:

Since dice has finite number of outcomes so each time when a dice is rolled it has finite variance.

So rolling a dice will have normal distribution in the long run.

2:

Mean is a measure of central tendency that is affected most in case of outliers.

3:

The mean is:

4:

Let a shows the 11th number.

The total of first 10 numbers :

New sum:

The mean is:

orchestra answered 2 years ago

Consider a random experiment of rolling 2 dice. What is probability of rolling a sum larger...

Consider a random experiment of rolling 2 dice. What is probability of rolling a sum larger than 9? Select the best answer. A. 0.5 B. 0.1667 C. 0.2333 D. None of the above

R Questions Question 2 In an experiment of rolling 10 dice simultaneously. Use the binomial distribution...

R Questions Question 2 In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings: a) The probability of getting six 6's ```{r} #INSERT YOUR ANSWER HERE ``` b) The probability of getting six, seven, or eight 3's ```{r} #INSERT YOUR ANSWER HERE ``` c) The probability of getting six even numbers ```{r} #INSERT YOUR ANSWER HERE ``` ****** ## Question 3 In a shipment of 20 engines, history shows that the probability of any...

1.) In rolling a pair of dice, what is the probability of a total of 4...

1.) In rolling a pair of dice, what is the probability of a total of 4 or less? 2.) A blue die and a red die are tossed together. Find the probability that the sum is less than 7, given that the blue die shows a 3. 3.) A fair coin is tossed three times. Find the probability of getting at least two tails, given that the first toss is tails.

In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings:...

In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings: a) The probability of getting six 6’s b) The probability of getting six, seven, or eight 3’s c) The probability of getting six even numbers

1. Many games require rolling 2 dice and adding the rolls together. Fill in the table...

1. Many games require rolling 2 dice and adding the rolls together. Fill in the table below with the sum of the two die rolls. The first few cells have been completed as an example. Sum of Die Rolls First Die Roll 1 2 3 4 5 6 Second Die Roll 1 2 3 4 2 3 3 4 5 6 a. We assume die rolls are all equally likely. There are 36 possible outcomes (6x6) when we give them...

Consider a rolling two four-sided dice with faces 1, 2, 3 and 4. (a) Obtain the...

Consider a rolling two four-sided dice with faces 1, 2, 3 and 4. (a) Obtain the pmf of X where X is the sum of the two resultant faces (b) Suppose the two die were rolled many times. Approximately, what would would be the average of X? (c) Calculate the standard deviation of X.

Rolling doubles When rolling two fair, 6-sided dice, the probability of rolling doubles is 1/6. Suppose...

Rolling doubles When rolling two fair, 6-sided dice, the probability of rolling doubles is 1/6. Suppose Elias rolls the dice 4 times. Let W = the number of times he rolls doubles. The probability distribution of W is shown here. Find the probability that Elias rolls doubles more than twice. Value 0 1 2 3 4 Probability 0.482 0.386 0.116 0.015 0.001

Let X be the sum of rolling 2 dice. a) Plot the CDF and PMF of...

Let X be the sum of rolling 2 dice. a) Plot the CDF and PMF of X. b) Determine P(5 < X <=8 | x<=10) c) Determine the median, mean and variance of X d) Bonus: Compute the correlation between X and Y = the number on the first dice.

a) A pair of fair dice is thrown. What is the probability of rolling a value...

a) A pair of fair dice is thrown. What is the probability of rolling a value between 8 and 11, inclusive? (Write your answer as a decimal rounded to 3 decimal places.) b) What is the probability of drawing a black face card when a single card is randomly drawn from a standard deck of 52 cards? (Write your answer as a decimal rounded to 3 decimal places.)

1. Consider rolling five dice. What is the probability of getting three ones (to 8 decimal...

1. Consider rolling five dice. What is the probability of getting three ones (to 8 decimal places)? 2. Consider rolling five dice a single time each. What is the probability of rolling six ones?