## A coffee dispenser pours cups of coffee automatically. We know that the amount paid in a cup follows a normal law.

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1. A coffee dispenser pours cups of coffee automatically. We know that the amount paid in a cup follows a normal law. To check the machine's calibration, a technician brought out a sequence of cups and got the following quantities:

Quantity (in ml) in the cup of coffee

305 310 296 300 298 285 306 310 315 295 308 299 300 310 305

Estimate the average amount paid by a confidence interval at the 90% confidence level

2. Maclean’s magazine poll of 352 subscribers reveals that on average they spend 13.4 hours per week on the Internet, with a standard deviation of 6.8 hours. Give an estimate by confidence interval of the average time of Internet use at the subscribers of this magazine at the 85% confidence level.

a) Write in terms of probability for the region next hatched under a centered-reduced normal distribution curve. Then determine the value of this probability.

b) Find the dimension value z such that P (0 <Z <z) = 42%

4. In a chamber of commerce, members have a turnover distributed according to a

normal distribution with mean ? = 120 k \$ and a standard deviation ? = 18 ? \$

a) What is the z score of a member with a turnover of \$ 112k?

b) From how much turnover are we in the richest 10%?

c) How much less does it take to be in the bottom 20%?

5. It is assumed that 60% of people prefer Coke to Pepsi. You select 15

random people for study.

a) What is the probability that exactly 8 people in the group prefer Coke to Pepsi?

b) What is the probability that at most 10 people prefer Coke to Pepsi?

c) What is the expected number of people who prefer Coke to Pepsi in this group?