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- 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.Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 38 minutes, but executives have good reason to believe that u is different from 38 minutes. The executives hire a statistical consultant and ask her to perform a statistical test. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 10 minutes. Based on this information, complete the parts below. (a) what are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test? Ho H₁ :0 (b) Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? (Choose one) ▼ (c) Suppose the true mean shopping time spent by customers at the supermarkets is…
- Fourty six percent of the students in a class of 120 are planning to go to graduate school, Find the variance of this binomial distributionFind the variance of x or the number of cups of coffee. (Do not round intermediate steps but round your final answer to 4 decimal places)The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 1. Find the probability that a person will walt for less than 7 minutes. Round your answer to four decimal places. Answer esc If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. 1 hp angle. q a Z F @ 2 W S 320 3 e d C $ 4 r f % 5 V t g Normal Table - to-z Normal Table - to z 6 O Oll b y hp h & 7 O n u J - * 8 N O i m 9 k * O : Tables ctrl Keypa Keyboard Shortc Submit Answer { D + = ? Oct 27 11 } 5:21 8 back 1 USE YOUR SMARTIN Reviews - Videog Spass Sun
- Suppose that the probability that a patient admitted in a hospital is diagnosedwith a certain type of cancer is 0.03. Suppose that on a given day 10 patients areadmitted and X denotes the number of patients diagnosed with this type of cancer.Determine the probability distribution of the random variable X. Find the meanand the variance of XSoledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T. What is the probability that Soledad sends more texts on a randomly selected day? 0.104 0.214 0.786 0.896The owner of a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer. Round to two decimal places. X P(x) 1 0.05 O A. 0.56 OB. 3.97 OC. 3.57 OD. 1.95 2 3 0.19 0.20 4 5 0.25 0.12 6 0.10 7 8 0 0.08 9 10- 0 0.01