Statistical and probabilty questions part 1

Suppose that the time between ordering and receiving your order in quick takeaway fast food chains has been found to be normally distributed with a mean time f 10 minutes and a standard deviation of 2.5 minutes.

Q1. What is the probability that a randomly selected person will have to wait at least 6 minutes before his or her order is served

Q2. In an advertising campaign raylene brown the manager of quick take-away, offers a coupon for a free bottle of wine with the next purchase for al customers whose service time exceeds 10 minutes.

Q3. What proportion of customers would receive coupons if the process were improved so that the mean service time was reduced to 5.5 minutes and the stand deviation remained at 2.5 minutes?

Q4. Once the mean service time was reduced to 5.5 minutes, would RAylene be better off focusing on improvement that reduced the mean 4.5 minutes or improvement that reduced the standard deviation to 1.5 minutes. Explain the reasons for your answers.

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Attempted answers:

Q1 Using excel functions we notice the proportion of those who wait less than 6 minutes is 0.05479 or 5.479 % and that gives us the answer which is 0.9452or 94.52% of customers receieve the food in 6 minutes or more.

Q2 Using excel functions we notice that with the new info and the new proportion of those who would recieve a coupoun ( wait more than 10 minutes ) drops considerably because of the new improvements. The % of those who wait less than 10 minutes are 96.40% or 0.96407 which means that those who wait more than 10 minutes are only 3.6% of the total customers or 0.036 proportion.

Q3 Both reducing the mean or the St.deviation will be beneficial however, the standard deviation has a bigger impact on the result as it covers a more wider range of data.This can be demonstrated using the same example of the 10 minutes. With a smaller mean we get 0.986097 while with a smaller St.deviation we get a better result which is 0.99865.

Those are my answers and as a person who doesnt know about statistics mcuh am sure i have some wrong answers, so if you are fimiliar with stats and are able to tell me the right answer reply as I need the answers asap

Thank you

mayguy

Thank you

mayguy