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(Total 16 marks) 115. An automated coffee machine is set to dispense coffee into cups. The amount of coffee
dispensed by the machine into each cup can be regarded as being normally distributed, with a
mean of 330 ml and standard deviation of 6 ml.
(a) What is the probability that the amount of coffee dispensed into a cup exceeds 327 ml?
(2) (b) What amount is exceeded by 95 % of the cups?
(3) The vendor of this machine suspects that the machine is dispensing more than the desired
amount. For that purpose, she collects data about 60 cups and finds that the average amount per
cup was 332 ml.
(c) What is the probability that this machine with its current settings can give a sample with
average 332 ml or higher?
(3) 80 (d) Hence or otherwise, test at the 5 % level of significance, the vendor's
hypothesis that the machine is dispensing more than the desired amount of 330 ml.
(3) Still not convinced of the results, the vendor asks one of her managers to measure the
amount of coffee in a random sample of 25 other cups. The results were as follows:
334.993
342.208
330.679
331.612
324.537 (e) 342.237
329.612
331.704
341.288
337.487 327.654
336.626
330.974
318.524
335.379 336.643
338.207
334.564
333.665
330.758 326.982
329.834
324.996
335.889
332.540 Given that this sample has a mean of 332.78 ml (correct to 2 decimal
places), find a 95 % confidence interval for the true population mean.
Give your answer correct to 2 decimal places.
(4) (f) Hence or otherwise test, at the 5 % level of significance, the
hypothesis that the machine is not dispensing the required amount.
(2) (g) Another objective of this second exercise is to determine whether the
proportion of cups that are overfilled is more than 0.5. Find a 95 %
confidence interval for the true proportion of cups that have more coffee than the
vendor desires.
(4)
(Total 21 marks) 81 116. In an effort to study the level of intelligence of students entering college, a psychologist
collected data from 4000 students who were given a standard test. The predictive norms for this
particular test were computed from a very large population of scores having a normal
distribution with mean 100 and standard deviation of 10. The psychologist wishes to determine
whether the 4000 test scores he obtained also came from a normal distribution with mean 100
and standard deviation 10. He prepared the following table (Expected frequencies are rounded
to the nearest integer):
Score
≤ 70.5 20 70.5–80.5 90 80.5–90.5
90.5–100.5
(a) observed
frequencies expected
frequencies Score observed
frequencies expected
frequencies 6 100.5–110.5 1450 96 110.5–120.5 499 507 575 120.5–130.5 80 76 1282 ≥ 130.5 4 4 Copy and complete the table, showing how you arrived at your answers.
(5) (b) Test the hypothesis at the 5 % level of significance.
(6)
(Total 11 marks) 117....
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.
 Fall '13
 Apple
 The Land

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