State, with reasons, which of the standard distributions might serve as models for: i. The number of particles emitted in 10 second intervals by a sample of radioactive material. ii. The number of times individuals take their driving test before passing. Indicate which conditions supporting the distribution may not be satisfied in each case.

explains the process :)

1. A random variable, X, follows a hypergeometric distribution with N=50, a=10 and n=6. Which of the following is NOT a possible value for X? A. 0 A. 25% 2. A random variable, X, has a mean of 100 and variance of 64. Which of the following is not a possible value for P(84 8) C. 6 A. binomial 3. It is known that the number of misprints on a textbook page follows a Poisson distribution with a mean of 0.004. Which of the following is the standard deviation of the number of misprints on a textbook of 475 pages? B. 0.063 C. 85% D. 10 C. 1.9 D. 95% 4. X is a discrete random variable, which of the following quantities is the same as P(X2 8)? B. 1-P(X 8) 5. Which of the following random variables could have a variance greater than its mean? C. geometric B. hyper-geometric D. 1.378 D. 1- P(X≤8) D. Poisson

Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the ________. A) t-distribution with df = 82 B) t-distribution with df = 81 C) t-distribution with df = 41 D) t-distribution with df = 80

Solve. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of the random variable X + Y. Round to two decimal places if necessary. Mean SD 41 8 Y 41 12 O A. µ= 82 and o = 14.422 O B. u = 82 and o = 9 O C. µ= 41 and o = 10 O D. µ=41 and o = 14,422 O E. µ= 82 and o = 20 Click to select your answer. MacBook Air FIO 20 F3 F7 esc 000 F4 FS

3. A sample of 20 items from a population with an unknown o is selected in order to develop an interval estimate of u. Which of the following is not necessary? A. We must assume the population has a normal distribution. B. We must use t distribution. C. Sample standard deviation must be used to estimate the population standard deviation. D The sample must have a normal distribution.

3. Determine the following from the graph. Show all your work. a. Determine the mean and standard deviation: PDF of a Random Variable ū 6.09 COM 0.04 · b) Draw a qualitative sketch of the CDF of the distribution shown. Be sure to show axis values and key values that are appropriate! 0 10 c) What type of distribution was the PDF of a Random Variable?

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 Ib, the boat was rated to carry 70 passengers (so the load limit was 9,310 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 133 lb to 174 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with mean of 181.1 Ib and a standard deviation of 38.6 lb. Find the probability that the boat is overloaded because the 70 passengers have mean weight greater than 133 lb The probability isO: (Round to four decimal places as needed.) b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,958 Ib. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 (so that their total weight is greater than the maximum capacity of 2,958 Ib). The probability is. (Round to four decimal places as needed.)…

A random sample of size 25 is to be taken from a population that normally distributed with mean 60 and standard deviation of 10. The mean sample of observation in our sample is to be computed. The sampling distribution of x ___ A.   is Normal with mean 60 and standard deviation 2.   B.   has unknown shape with mean 60 and standard deviation of 2   C.   is approximately Normal with mean 60 and standard deviation 10.   D.   is Normal with mean 60 and standard deviation 10.

5.79 Suppose x is a binomial random variable with p = 4 and n = 25. NW