statistics questions 4

– 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_ ‘i_r~~p.e:c,:t, how many

different sets of 13 stations would exist?

d. If all sets were equally likely, what is the probability of each set?

– 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?

– Since careful records have begun being kept in January, Eric’s small business has

delivered the following quantities of flowers throughout town.

January February March April May June July August

BSomuaqllu ets 85 34 26 24 43 29 30 19

LBaorugqeu ets 23 64 27 18 33 23 20 13

– Assuming the data is normally distributed, _Eonstruct 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.

quality control experiment is to be done on a machine that fills tubes with toothpaste.

Its specifications require that it fill tubes with 4. 7oz. 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 subtracted from each:. Pertorm a hypothesis

test at the 90% confidence level to determine if the machine is performing according to

specifications.

4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.7b 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