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Math Help - 10 Prob and Stats Problems I have been struggling with...please help

  1. #1
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    10 Prob and Stats Problems I have been struggling with...please help

    1. Assume blood pressure readings are normally distributed with a mean of 120 and standard deviation of 8. What percentage of people have a blood pressure reading greater than 145?

    2. Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $41,000 and a standard deviation of $4,000. What is the cut-off salary for teachers in the bottom 10%?

    3. A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces?

    4. A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distributions to approximate the binomial distribution.

    5. A random sample of 150 students has a test score average with a standard deviation of 0.78. Find the error of the estimate if c=0.98.

    6. In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of $22.50. Assume the distribution of weekly food expenses is normally distributed.

    7. A brewery claims that the mean amount of beer in their bottles is at least 12 ounces. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

    8. The dean of a major university claims that the mean time for students to earn a Master's degree is at most 5.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

    9. Given H naught: with a mean greater than 85 and P-Value=0.006. What is the decision at the 0.01 level of significance?

    10. Find the critical t values for a sample with n=15 and a=0.05 if H null: with a mean less than or equal too 20.

    I greatly appreciate any one's help. These are problems I have struggled with this semester....and now that the end is winding down I would love to figure them out for future references. Thank so much to everyone!
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    Please post any attempts you have made on these questions. It will help us help you better.

    Quote Originally Posted by loutja35 View Post
    1. Assume blood pressure readings are normally distributed with a mean of 120 and standard deviation of 8. What ve to figure them out for future references.
    Find P(X>145) = P\left(Z>\frac{145-120}{8}\right)= P(Z>3.125)
    Last edited by pickslides; December 2nd 2009 at 07:10 PM. Reason: bad latex
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  3. #3
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    Thanks for your input!

    Sorry about that, I wasn't thinking my work would help much. My thoughts are that because the blood pressure reading is greater than 145, that we would have to subtract 1 from it because it would be on the right side of the z score, and it has to be on the left side (so we subtract one). I'm not sure if what you put down is the right answer. This was also a multiple choice question and the choices were
    a. 99.91%
    b. 0.09%
    c. 6.06%
    d. 11.09%

    I have tried multiple ways to figuring out this problem and still do not get any of these multiple choice answers. Once again thank you so much for your help, it is truly appreciated!
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  4. #4
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    This has to be the answer as the other answers are not even close

    Quote Originally Posted by loutja35 View Post
    a. 99.91%
    Consider P(\mu-3\sigma < Z <\mu+3\sigma) \approx 0.99
    Last edited by pickslides; December 2nd 2009 at 07:43 PM. Reason: bad latex, bad latex day for me!
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  5. #5
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    Too many question in one thread.

    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. Start new threads as necessary for remaining questions. eg. If you have five questions, post two of them in two threads and start a new thread for the remaining one etc.

    And if the question has more than two parts to it, it is best to post only that question and its parts in the thread and start a new thread for other questions.
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