A regular six-faced fair die will be rolled 144 times. Let X be the sum of...

A regular six-faced fair die will be rolled 144 times. Let X be the sum of the 144 numbers obtained. Find the approximate probability that X is between 463 and 545.

Expert Solution

TOPIC:Use of the Central limit theorem to find the required probability.

orchestra answered 2 years ago

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine...

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine the probability distribution for the sum of the two dice. Create a frequency histogram for the probability distribution and determine the expected sum of the two dice.

A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let...

A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let X denote the number of rolls required until the third 6 is rolled. Find the probability that fewer than 5 rolls will be required to roll a 6 three times.

Example 4: A fair six-sided die is rolled six times. If the face numbered k is...

Example 4: A fair six-sided die is rolled six times. If the face numbered k is the outcome on roll k for k = 1, 2, 3, 4, 5, 6 we say that a match has occurred. The experiment is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The outcome space is O = {success, failure}. Let event A = {success}. Which value has P(A)? **This question has...

A fair 4-sided die is rolled, let X denote the outcome. After that, if X =...

A fair 4-sided die is rolled, let X denote the outcome. After that, if X = x, then x fair coins are tossed, let Y denote the number of Tails observed. a) Find P( X >= 3 | Y = 0 ). b) Find E( X | Y = 2 ). “Hint”: Construct the joint probability distribution for ( X, Y ) first. Write it in the form of a rectangular array with x = 1, 2, 3, 4 and...

A fair die is rolled twice. Let X and Y be the smallest and largest, respectively,...

A fair die is rolled twice. Let X and Y be the smallest and largest, respectively, number that appears in the two rolls. (a) Determine the probability mass function of (X, Y). (Write a formula forP(X=i, Y=j)or give a table of values.) (b) Are X and Y independent? (c) Find E(X+Y). (Give your answer as a decimal number.)

A fair die is rolled twice. Let X be the maximum of the two rolls. Find...

A fair die is rolled twice. Let X be the maximum of the two rolls. Find the distribution of X. Let Y be the minimum of the two rolls. Find the variance of Y.

A balanced die with six sides is rolled 60 times. For the binomial distubtion of X...

A balanced die with six sides is rolled 60 times. For the binomial distubtion of X = Numbers of 6’s, what is n, what is p, and what is q Find the mean and standard deviation of the distribution of X. What do these values tell you? If you observe X = 2, would you be skeptical that the die is balanced? Explained why, based on the mean and standard deviation of . How long would the value of X...

2. Three fair dice are rolled. Let X be the sum of the 3 dice. (a)...

2. Three fair dice are rolled. Let X be the sum of the 3 dice. (a) What is the range of values that X can have? (b) Find the probabilities of the values occuring in part (a); that is, P(X = k) for each k in part (a). (Make a table.) 3. Let X denote the difference between the number of heads and the number of tails obtained when a coin is tossed n times. (a) What are the possible...

A fair coin is tossed, and a fair die is rolled. Let H be the event...

A fair coin is tossed, and a fair die is rolled. Let H be the event that the coin lands on heads, and let S be the event that the die lands on six. Find P(H or S).

Let Y be the sum of two fair six-sided die. (a) Find the PMF of Y....

Let Y be the sum of two fair six-sided die. (a) Find the PMF of Y. (b) What is the expected value of Y ? (c ) What is the standard deviation of Y ? (d) Interpret the standard deviation you found in the last part in context of the experiment. (e) Find the CDF of Y. (f) Use the CDF of Y to find the probability that the sum of the dice will be strictly between six and ten....

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