Number 11,12,and 13 Name:Essay912.The principal at a local high school asked 100 randomly selected students how many minutes they spendcompleting homework each night of the week. The mean time students in the sample spent on homeworkeach night was 72.5 minutes. Assume the population mean time spent on homework cach night is 81.2s. Which of the following is the correct representation of the mean time spent on homework for the100 randomly selected students in the sample and the population of students at the school?72.5 minutes and pr 81.2 minutes, both are parameters.72.5 minutes and 7-83.2 minutes, 72.5 is a parameter, but $1.2 is a statistic.7-72.5 minutes and -81.2 minutes, 72.5 is a statistic, bot 81.2 is a parameter.7-72.5 minutes and 7-81.2 minutes, both are statistics.b.10A manufacturer claims that only 25% of their products are defective. A store receives a delivery of 300 itemsfrom the manufacturer. Let the proportion of defective items in a sample of 300 items. Assuming themanufacturer is correct that only 25% of their products are defective, what are the mean and standarddeviation of the sampling distribution of 7The mean is 0.02 and the standard deviation is 0.008.C.4.C.ab.c.d.11. The mean number of items purchased by shoppers at a grocery store is strongly skewed right with a mean o14.5 and a standard deviation of 8.6. A random sample of size 100 will be selected. What is the mean andstandard deviation of the number of items purchased by shoppers in all possible samples of that size?a.ID: BThe mean is 6 and the standard deviation is 2.42.The mean is 6 and the standard deviation is 5.88.The mean is 0.02 and the standard deviation is 0.196.The distribution of the age of the employees at large manufacturing plant is strongly skewed left with a rof 42.19 years old and a standard deviation of 9.86 years old. The manager of the manufacturing plant pto select a random sample of 35 employees to survey about their attitudes towards management and worethics.b. What is the approximate probability that the mean age for a sample of size n-35 is no more thayears old?Based on your answer to the part (b), would you be surprised if the manager selected a samplesample mean was no more than 40 years old? Explain.What is the shape of the sampling distribution of X, the sample mean age of the employees for sarsize n = 35?13. The amount of money customers at a local restaurant spend per meal is approximately normally cwith a mean of $20.91 and a standard deviation of $6.13. The manager plans to select a randomcustomers to survey the quality of the service the restaurant offers.Calculate the mean and standard deviation of the sampling distribution of x, the sample memoney spent per customer at the restaurant for samples of size n = 10.b. Interpret the standard deviation of the sampling distribution calculated in part (a).C.The manager believes that if a customer spends more than $25, the customer will have aopinion of the service the restaurant offers than if a customer does not spend more thanthe probability that in a random sample of 10 customers, the sample mean would be mc3

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