Download Probability Distributions and Z-Scores in Statistics - Prof. Patrick S. Murphy and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity!
1
That old refrigerator…
- The lifetime of a refrigerator is a normal distribution with a mean of ten years and a standard deviation of 1.5 years. a) Sketch the distribution of X which represents the lifetime of this particular brand of refrigerator.
b) What percentage of refrigerators last between 6.2 and 9.1 years?
c) What percentage of refrigerators last more that 12 years and 6 months?
d) What percentage of refrigerators last less than 5 years?
e) Would it be highly unlikely for a refrigerator to last less than five years? Justify your answer.
f) How long does a refrigerator last if its lifetime is not in the upper 10%?
g) How long does a refrigerator last if its lifetime is in the MIDDLE 50%?
2
- Sketch the area on the Standard Normal Curve that represents the probability of the following events and then determine with your calculator the probability.
a) 0.89 < Z < 2.11 b) Z ≥ -1.33 c) Z < -1.
- A z-score tells us how many standard deviations a particular value is from the mean. Assume that exam scores are normally distributed. An instructor gives an exam where the mean is 78 and the standard deviation is 8. a) Find the z-score for some one who makes 100 on the exam.
b) Find the z-score for someone who makes a 70 on the exam.
c) If you make a 90 on the exam, how many standard deviations above the mean are you?
d) If I tell you that you are 2 standard deviations below the mean, what grade did you make?
e) Use the z-score formula to verify that an exam score of 74 corresponds to a z- score of − 0. 5.
