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- A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.5 4.1 4.7 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value Find (or estimate) the P-value. A. P-value > 0.250 B. 0.125 < P-value < 0.250 C. 0.050 < P-value < 0.125 D. 0.025 < P-value <…Determine the value/s of the random variable in each of the following situations: 1. A family has three children. Let W be the number of boys in the family A. 3 B. 1 C. 0 D. 0, 1, 2, 3 E. 0, 1, 2 F. 0, 1 G. 2An insurance company covers 100$ per day for the first day of staying in a hospital, and 50$ per day for any day after the first day if any. The number of days the patients used to stay in the hospital is a random variable with PMF: 6-k k = 1, 2, 3, 4, 5 Px(k) = 15 else the expected amount the company will pay is: Select one: а. 230 b. 166.67 c. 233.33 d. 220 e. 200
- A company produces 10,000 bags per day. This company supplies bags to a shop which sells them in packs of 10 bags per pack. If less than two of a randomly selected pack (of 10 bags) from the order are defective, the shop accepts the whole order. The proportion of defective bags produced by the manufacturing company is 10%. Let ? be the random variable representing the number of defective bags in a pack.i. Identify the type of distribution being described in this question and write down the value/s of its parameter/s.ii. What is the probability that the order will be accepted?iii. What is the probability that a randomly selected pack (of 10 bags) has more than two defective bags?There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable Z is the sum of X and Y. That is, Z = X + Y. Calculate the mean of Z.In a study, it was found that 42.5% of the population drink soda at least once a day. You randomly select 8 people. Let X be the number of people in the sample that drink soda at least once a day.Then X has what distribution?
- When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinneThe probabilities of all the values of a random variableX must: OA. average to a small and negative number. OB. add up to 1. OC. average to 0. D. none of the above,An insurance company covers 100$ per day for up to three days staying in a hospital, and 50$ per day for any day after the first three days if any. The number of days the patients used to stay in the hospital is a random variable with PMF: 6-k k = 1, 2, 3, 4, 5 Px(k) =. 15 else the expected amount the company will pay is: Select one: а. 220 b. 230 c. 166.67 d. 233.33 е. 200
- Three students scheduled interviews for summer employment at the Tiket.com. In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews.a. List the experimental outcomes.b. Define a random variable that represents the number of offers made. Is the random variable continuous?c. Show the value of the random variable for each of the experimental outcomesA test of 100 motor is done to determine the defective motors. The probability that a motor is defective is 0.02. The motors defects are independent random variable. The probability that exactly two motors are defective given that the number of defective motors is two or fewer is: Select one: a. 0.3127 b. 0.5846 c. 0.5364 d. 0.404 e. 0.47734. A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Yı = 0, if the policy holder does not have any health issues; Yı = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).