POISSON DISTRIBUTION9) In a city, one out of 50 adults smokes cigarette. A random sample of 120 adults werechosen. Using Poisson approximation, find the probability that at least four adultssmoke cigarette.10) By referring to Q9), n sample of adults were chosen randomly. Find the smallestvalue for n that the probability of at least one adults smoke cigarette exceeds 0.9.

Given that, In a city, one out of 50 adults smokes cigarette. A random sample of 120 adults were…

Answered: 9) In a city, one out of 50 adults…

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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There are two car battery producers, such as A and B. The mean lifetimes of batteries are 1424 and 1624days from the producers of A and B, respectively. The standard deviations of the batteries from both manufacturers are 200 and 100 days for A and B, respectively. Random samples of 120 batteries from each company are selected for the test.a) Please find the probability for the Brand A batteries that the average lifetime is at most 960 days.b) Find the probability for the Brand A batteries that the average lifetime is 150 days more than the batteries from Brand B.
Q 4: Mr. Ahmed who is a manager at PVR Multiplex Muscat has conducted a survey to investigate the number of people visited the theatre in the last 30 days. The number of people visited the theatre in the last 30 days are: 30, 36, 39, 37, 36, 54, 38, 33, 37, 33, 33, 36, 32, 48, 42, 38, 36, 35, 30, 33, 39, 37, 33, 36, 30, 39, 44, 32, 44 and 50. Find out the grouped frequency distribution using 5 classes. Which graph will be suitable to present the grouped frequency distribution? Give reasons to your answer Cumulative frequency and relative frequency are same. Discuss critically
5. Suppose that the number of insects caught in a spider's web in one day follows a Poisson distribution with rate = 2.6. For the questions that follow, make sure to define a random variable, state its distribution (including parameters), and translate the question into a probability statement. %3D wg probal b What is the probability that the spider catches at least one insect in 12 hours? PUS 18)
Find conditional probability Find mean and standard deviation 11)The age of customers at a local hardware store follows a uniform distribution over the interval from18 to 60 years old. Find the average age of customers to this hardware store. 140). 12) Suppose x is a uniform random variable with a = 20 and b = 80. Find the standard deviation of x. Find mean and standard deviation
16. For a recent period of 100 years, there were 530 Atlantic hurricanes a) State the distribution, the parameters (for each case) and the support of the distribution. b.) Find the probability that over a period of 2 years there are fewer than 5 hurricanes. c.) Find the probability that over a 5 year period there are 10 hurricanes. d.) Find the probability that at least 2 hurricanes happen in a year.
Suzette does an experiment where she collects date from 5 women snd obtains the scores: 4, 4, 5, 2, 5. She hypothesizes that the population mean for the population from which these scores are drawn is 3. She wants to test whether this hypothesis is true. What is the alternative hypothesis she is testing?
A random variable follows a binomial distribution with the probability of success for one trial at 0.745 and 18 randomly selected trials. Round to the fourth. a) Find the mean of the distribution. b) Find the standard deviation of the distribution c) Find the probability of exactly 13 successes.
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.50. Assume that the groups consist of 32 couples. A) Find the mean and the standard deviation for the numbers of girls in groups of 32 births.
A committee with 3 members is to be chosen randomly from 5 boys and 7 girls and count the number of girls on the committee. a) Identify the two groups. b) In words, describe the random variable X. c) List the values of the random variable X takes on. d) What is the expected number of girls on the committee? e) Determine the standard deviation of the number of girls in the committee.
Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?
The length, X, of a lionfish is a normally distributed random variable with a mean of 13.5 inches and a standard deviation of 2.4 inches. Suppose that we measure the lengths of 150 randomly chosen lionfish. Let M be the sample mean of the 150-length measurements. Let S be the sum of the 150 length measurements.a) What is the probability that X < 9.3? b) What is the probability that X > 9.3? c) What is the probability that all of the 150 measurements are greater than 9.3? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-150*13.5 >10? g) What is the standard deviation of S-150*13.5 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >13.6? k) What is the standard deviation of 30*M? l) If the probability of X > k is equal to .8, then what is k?

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