A group of players is playing a game involving a special set of dice. A success ona single roll has a probability of 35.5%.a. An experiment is conducted by performing this roll 24 times and countingthe number of successes. Is the normal approximation to the binomialtheorem appropriate for this experiment?b. Regardless of your answer to part a, use the normal approximation to thebinomial theorem to find the probability of getting more than 10 and fewerthan 15 successes in 24 rolls.

Given that probability of success of a single roll of dice is 35.5% (0.355).p = 0.355Number of rolls…

Answered: A group of players is playing a game…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a game, you have found a reward with 15 treasure boxes. From experience you know that 1 in 5 treasure boxes contain rare items. a. You want to know the probability of having 4 rare items in your 15 treasure boxes. Can the normal approximation to the binomial distribution be used? Justify your answer and describe why it is important to check that the normal approximation can be used. ( b. If you instead had 50 treasure boxes, could the normal approximation to the binomial distribution be used?
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.Do you try to pad an insurance claim to cover your deductible? About 37% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 126 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.) (a) half or more of the claims have been padded(b) more than 80 of the claims have not been padded
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 39 and p = 0.20. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q =
Show all work. Suppose that 52% of residents of Union County, NC have brown eyes. a) if you were to select a simple random sample of 8 people from this population, and you wanted to find the probability that fewer than two of the 8 would be brown-eyed, why would it not be appropriate to use a normal (z) approximation? Explain b. Use the binomial probability formula to calculate the probability that if you were to select a simple random sample of 8 people from this population, fewer than two of them would have brown eyes. c. Use the normal (z) approximation of the binomial distribution to find the probability that if you were to select 80 people at random from this population, at least 50 of those people would have brown eyes.
Consider a binominal experiment with 2 trials, and p=0.4 d. Find the probability of at least one success
A process produces strings of Christmas tree lights that historically have experienced a defective rate of 4%. A customer has placed an order for 140 strings of lights. Use the normal approximation to the binomial distribution to answer parts a through e. d. What is the probability that 4, 5, or 6 strings in this order will be defective? The probability is nothing. (Round to four decimal places as needed.)
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 30 and p = 0.25. (For each answer, enter a number. Use 2 decimal places.) What are the values of ?p̂ and ?p̂? (For each answer, enter a number. Use 3 decimal places.)?p̂ = mu sub p hat = ?p̂ = sigma sub p hat = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blank YesNo second blank cancannot third blank both n·p and n·q exceedn·p exceeds n·q exceedsn·p and n·q do not exceedn·p does not exceedn·q does not exceed fourth blank (Enter an exact number.) (c) Suppose n = 53 and p = 0.26. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal…
A company surveyed 2,600 North American airline passengers and reported that approximately 70% said that they carry a smartphone when they travel. Suppose that the actual percentage is 70%. Consider randomly selecting ten passengers and define the random variable x to be the number of the ten selected passengers who travel with a smartphone. The probability distribution of x is the binomial distribution with n = 10 and p = 0.7. (Round your answers to three decimal places.) (a) Calculate p(8). p(8) = (b) Calculate P(x ≤ 6). P(x ≤ 6) = (c) Calculate the probability that more than half of the selected passengers travel with a smartphone.
2) A particular NBA player is a career 59% field goal shooter. If he takes 50 shots, find: a) the probability he makes at most 30 using the normal approximation to the binomial. b) the probability he makes exactly 28 using the normal approximation to the binomial.
In a game, the gamer wins 20 dollars if he gets the number "6" facing up in rolling a fair die; he needs to pay c dollars otherwise. The gamer decided to continue playing the game until he wins three times. If the expected gain of the gamer is 0 dollars, what is the value of c? [This question seems to be a negative binomial distribution question]
Find the indicated probability for a binomial random variable X. Round your answer to three decimal places, e.g. 0.628. P(X is no more than 1) when the number of trials (n) is 15 and the probability of success (p) is 0.2.
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 37% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 126 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.) A USE SALT (a) half or more of the claims have been padded (b) fewer than 45 of the claims have been padded (c) from 40 to 64 of the claims have been padded (d) more than 80 of the claims have not been padded

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