Answer Question 4: Your real Final exam will follow the style, format and conten

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Answer Question 4:

Your real Final exam will follow the style, format and content of this exam closely. Answer each question folly. Please, be neat and label everything necessary. Calculators may be used, as well as the FABLES from the book. Use additional paper if necessary. Copies of these TABLES will be provided on exam day. The pulse rates of women are normally distributed with a standard deviation of 12.5 beats per minute. A medical group samples the pulse rates of 100 women they see during one day and find their mean to be 74.4 with a standard deviation of 11.7 beats per minute. Use a 0.05 significance level to test the claim that the sample does come from a population with mean equal to 74 beats per minute. A simple random sample at the local universities asks 1486 college students seeking bachelor's degrees whether they will graduate within 5 years. 802 of these students said that yes, they will graduate within 5 years. Use a 0.01 significance level to test the claim that most college students earn bachelor's degrees within five years. The load on a chair's leg before it can break is important in the construction of chairs. A chair manufacturer took a random sample of 175 chairs and found that their maximum load before breaking was 267.1 lbs with a standard deviation of 22.1 lbs. Use a 0.01 significance level to test the claim that these chairs have a mean maximum load less than 281.8 lbs. A bag contains colored cards: 3 Red, 7 Blue and 2 Yellow. Find the following probabilities: A. P(Red and Red) (Red card followed by second red card, with replacement) B. P(Blue and Blue) (Blue card followed by a second blue card, without replacement) C. P(Yellow and Red and Red) (Yellow, then red, and then another red, without replacement) D. Which events in parts A, B and C are Independent or Dependent? Why? Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and the results are given below for Fridays on the 6th of a month und Fridays on the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.

Explanation / Answer

4:

Total number of cards in the bag: 3+7+2 = 12

(A)

Since cards are drawn with replacement so each draw will be independent from other. Therefore requried probability is

P(red and red) = P(red)P(red) = (3/12)*(3/12) = 0.0625

(B)

Since cards are drawn without replacement so drawns are not independent.

P(first blue card) = 7/12

After first draw, out of 11 remaining cards 6 are blue so

P(second blue|first blue) = 6/11

So required probability is

P(second blue and first blue) = P(second blue|first blue) P(first blue) = (6/11) *(7/12) = 0.3182

(C)

P(Yellow and Red and red) = (2/12) * (3/11) * (2/10) = 0.0091

(D)

Event of part A is independent and events of part B&C are dependent.

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