Fall 2011Math 227FinalName: ______

Show your work clearly, neatly, and understandably. Make sure you round the decimal for probability to 5-decimal place and round the percentage to 3-decimal. There are 105 points available.

  1. (27:6,1,1,1,1,1,3,1,6,6) Perform the first extension and second extension on the following frequency distribution of a sample data: (you may need only 3 columns, depending on your second extension)

xi / freq (fi)
5 / 2
6 / 3
7 / 5
8 / 6
9 / 4

After completing the frequency distribution, answer the following:

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  1. mean
  1. median
  1. mode
  1. Q1
  1. Q3
  1. variance
  1. standard deviation
  1. Construct a 94%-CI for μ:
  1. Construct a 95%-CI for σ:

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  1. (11:2,2,2,5) P(A) = 40%, P(B) = 45%, P(B|A) = 20%. Find

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  1. P(A and B)
  1. P(A or B)
  1. P(A|B)
  1. P(B|Ac)

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  1. (11:4,4,3)Eskimo Electric Corp. manufactures refrigerators. The lifetimes of these refrigerators are normally distributed, averaging 8.5 years with a standard deviation of 1.7 years.
  2. The company guarantees the refrigerators to last at least 6 years. What percent of all buyers will see their refrigerators fail before the guarantee ends?
  1. Of 10 refrigerators manufactured by this company, find the probability that at least 2 of them will have their refrigerators fail before the guarantee ends?
  1. How long (at least) do the best 20% of refrigerators last?
  1. (15:3,5,7) A box contains 10 identical marbles (except in colors): 5 blue, 3 yellow, and 2 green.
  2. Three marbles are selected with replacement. Find the probability of selecting 2 or more yellow marbles.
  1. Create a probability distribution of the number of blue marbles selected for a procedure of selecting three marbleswithout replacement.
  1. Copy the probability distribution from part (b) below and extend it to find the mean and the standard deviation.

SLO (3)The US Marine Corp has a height requirement for male enlistee (age 18-27 years old) between 58 in to 78 in tall. Male’s heights are normally distributed with a mean of 68.7 in. and a standard deviation of 2.5 in. What percentage of men meets that requirement? Draw a density curve with all relevant information.

  1. (13:2,3,8) Let X be the travelling time from home to work for a randomly chosen office-worker in Los Angeles. Assume that X has a normal distribution. A sample of 6 observations from this population gave the following times (in minutes): 35, 20, 25, 15, 22, and 21
  2. Find a point estimate for the population mean µ
  1. Find a point estimate for the population standard deviation σ.
  1. Test the claim, at 5%-SL, that σ = 8.
  1. (10)In a study on the effects of sodium restricted diets on hypertension, 24 out of 55 hypertensive patients were on sodium restricted diets, and 36 out of 149 non-hypertensive patients were on the same sodium restricted diets. Test the hypothesis that the proportion of patients on sodium restricted diets is higher for hypertensive patients than non-hypertensive patients.
  1. (6) In some states the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that only between ¼ and 1/3 (inclusive) of all drivers follow this rule. He wants to construct a 98% confidence interval for the proportion of all drivers who turns on their headlights when driving in the rain. How many cars driving in the rain does he need to examine so that the margin of error has a width of no more than 0.035?
  1. (9)A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are shown in the table. The "before" value is matched to an "after" value.

Subject: / A / B / C / D / E / F / G / H
Before / 6.6 / 6.5 / 9.0 / 10.3 / 11.3 / 8.1 / 6.3 / 11.6
After / 6.8 / 2.4 / 7.4 / 8.5 / 8.1 / 6.1 / 3.4 / 2.0

At 5%-SL, test the claim that hypnotism is effective in reducing pain?

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