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?

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