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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 45 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 39 and 63 ounces? c) What percentage of the widget weights lie above 33 ?\fWe are going to calculate the standard deviation for the following set of sample data. 4, 10, 15,4, 13 1) First, calculate the mean. D = 2) Fill in the table below. Fill in the differences of each data value from the mean, then the squared differences. 3) Calculate the standard deviation. - 4 10 15 4 13 TotalThe maintenance department at the main campus of a large state university receives daily requests to replace fluorecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 45 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 45 and 53? Do not enter the percent symbol. ans =Calculate the sample standard deviation of the data shown. Round to two decimal places. X 17 20 27 14 18 13 19 sample standard deviation =In a student's chemistry class, the final grade is based on six categories. The categories, grades, and weights are shown in this table. Category Grade Weight % Test 1 90 18 Test2 75 19 Test 3 56 20 Homework 53 9 Semester Project 57 8 Final Exam 63 26 Compute a weighted average to determine the student's overall final grade in the course. Record the overall final grade below as a percentage. Round accurately to two decimal places. Final Grade:The boxplots below shows salaries for Construction workers and Teachers. Construction Teacher 20 25 30 35 40 45 50 55 60 Salary (thousands of $) Q Jennie makes the median salary for a construction worker. Markos makes the first quartile salary for a teacher. Who makes more money? O Jennie O Markos How much more? $ (Note that the boxplots are labeled in thousands of dollars. For example, 30 means $30,000. If the difference appears to be $5, it is actually $5000. If this were the correct answer, you could enter it as either 5000 or 5,000)The table below shows the scores of a group of students on a 10-point quiz. Test Score Frequency 3 4 4 5 4 2 2 4 10 1 The mean score on this test is: The median score on this test is:The following refer to the following data set: 50.9 68.8 98.3 73 75.6 98.3 67.1 81.4 75.4 98.3 What is the arithmetic mean of this data set? mean = What is the median of this data set? median = What is the mode of this data set? mode =For the data shown, answer the questions. Round to 2 decimal places. 28.9 9.4 1.7 22.2 6.9 1.8 1.9 17.4 27.2 10.4 Find the mean: Find the median: Find the sample standard deviation