CSU Week 3 Normal Distributions Questionnaire

I'm working on a statistics question and need an explanation and answer to help me learn.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.

Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.

  1. The average score of a statistics class was 71 with a standard deviation of 8.
    1. What is the z score of a student with a grade of 68? (2.5 pts)
    2. What is the z score of a student with a grade of 80? (2.5 pts)
  2. Using the same data in #1 answer the following:
    1. Approximately 68% (one standard deviation) of the scores are between ________ and _________ (2.5 pts)
    2. Approximately 95% (two standard deviation) of the scores are between _________ and _________ (2.5 pts)
  3. Most values of the standard normal distribution are between __________. (3 pts)
    1. -3 and 3
    2. 0 and 1
    3. 0 and 3
    4. 1 and 3
  4. (a) If the standard deviation of a data set is 1.3, what is the variance? (2.5 pts)
    (b) If the variance is 36, what is the standard deviation? (2.5 pts)
  5. Let X have a normal distribution with mean µ= 20 and standard deviation σ = 4.
    Determine the area in the normal curve for which:
    1. P (X > 28) (2.5 pts)
    2. P (X > 12) (2.5 pts)
    3. P (X > 24) (2.5 pts)
  6. The IQ scores of students listed below are from a SAMPLE of MATH 300 class.
    IQ Scores 92 110 105 96 120 100 90 98 110 95
    102 99 93 119 106 103 91 101 97 105
    1. What is the mean IQ score? Round to the nearest whole number. (2.5 pts)
    2. Compute the IQ scores within plus/minus one standard deviation? Two answers. Round to the nearest whole numbers. (2.5 pts)
    3. Compute the IQ scores within plus/minus two standard deviation? Two answers. (2.5 pts)
  7. Let X have a normal distribution with µ= 10 and standard deviation σ= 2. Transform X to the standard normal form Z and match the following probability statements:

    a) P(X>14) 1) P(Z<-1)
    b) P(X<8) 2) P(-2 < Z < 2)
    c) P(6 < X < 14) 3) P(Z > 2)

    a) is matched to ___________ (2.5 pts)

    b) is matched to ___________ (2.5 pts)

    c) is matched to ___________ (2.5 pts)

  8. Let X have a normal distribution with mean µ= 30 and standard deviation σ= 10. Calculate P(X>40). Round to two decimal places. (4 pts)
  9. For a standard normal variable Z, compute P(Z<1.5). Round your answer to two decimal places. (3 pts)
  10. A larger standard deviation of a normal distribution indicates that the distribution becomes (2.5 pts)
    1. narrower and more peaked
    2. flatted and wider
    3. more skewed to the right
    4. more skewed to the left

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