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- From: Mathematics, Statistics and Probability
- Posted on: Mon 18 Jan, 2016
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1 A health inspector at a restaurant will enter the kitchen and choose 5 stations to inspect from a predetermined list of 15 stations present in most restaurant kitchens.
a. How many different sets of 5 stations exist?
b. If all sets are equally likely, what is the probability of each set?
c. If the inspector were instead to randomly select 13 stations .to inspect, how many different sets of 13 stations would exist?
d. If all sets were equally likely, what is the probability of each set?
2 The company policy for customer service representatives gives time off for positive reviews. If, in the first 20 calls a customer service agent handles In a day, 13 or more elect to take a subsequent survey and rate the service as "excellent," then the company gives the agent his or her final hour of work that day off, paid. Ellie receives excellent
reviews from about 30% of the calls she handles. Assuming she always receives at least 20 calls in the first 7 hours of a workday, on what percentage of her 8-hour workdays does Ellie get the final hour off?
3. When the owner of a small business reviews her list of contracts for 2011, she finds that 35% of the contracts were from clients she met at a large conference at the end of 2010. Answer the following questions about this situation
A Was this measurement obtained by a sample or a census? What words in the description of the situation make you confident that your answer is correct?
B. Should the owner have taken into account some measure of reliability associated with the value 35%.
4. Assume that the number of sales per day of an app in the Apple IOS App store is normally distributed.
A. What two parameters of the distribution would you need to be able to determine the probability of sales on a particular day exceeding 100 units?
B. If the probability of sales exceeding 100 units is 20% and the mean daily sales is 86 units, then what is the standard deviation of distribution?
5. Since careful records have begun being kept in January, Erics small business has delivered the following quantities of flowers throughout town
January February March April May June July August
Small Bouquets 85 34 26 24 43 29 30 19
Large Bouquets 23 64 27 18 33 23 20 13
Assuming the data is normally distributed construct two separate 90% confidence intervals one for the number of deliveries of small bouquets in September and one for the number of large bouquets in September.
6. Consider the following data values of a variable x and y
X 5,4,3,6,9,8,10
Y 7,8,10,5,2,3,1
Construct a scatter diagram for the data points and plot the least squares regression line on it. Find the least squares regression line.
7. A quality control experiment is to be done on a machine that fills tubes with toothpaste. Its specifications require that it fill tubes with 4.7 oz. A random sample of 40 tubes filled by the machine is taken and each tube is weighed. The resulting data are below, with the weight of the tube already having been subtracting from each. Perform a hypothesis test at the 90% confidence level to determine if the machine is performing according to specification.
4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56
4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75
4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74
4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69
Solution Description

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