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EDRM611: Applied Statistics

Homework for Statistics Lesson 4

Answer Completely.
 
Some calculations are required.
Due Fri., July 15, 2005, 10:30:00.000, EDT.
 
Due on the teacher's desk in BH114.
  1. Find the probability distribution for getting heads flipping four coins simultaneously (See Figure 4.1).

     

     

  2. Find the z-score for an IQ of 125 from a normal distribution with a mean of 100 and a standard deviation of 15. Show your work.

     

     

  3. Sketch the tail area to the right of the IQ in the problem above. What is this area (probability)?

     

     

  4. Describe completely an appropriate procedure for finding the area (probability) for the problem above.

     

     

  5. What IQ corresponds with the 90th percentile, assuming a mean of 100 and standard deviation of 15? Use the z-score formula in reverse after you have found the appropriate z-score in a normal distribution table.

     

     

  6. The empirical rule is basically only good to two significant digits. Express the empirical rule to four significant digits and four standard deviations.

  7. Suppose a high school has 200 freshmen with normally distributed IQs with mean 110 and standard deviation 14. How many of these students would you expect to have an IQ below 70? Above 130?

     

     

  8. What NCE-scores and percentiles correspond identically?

     

     

  9. John got a 31 on the ACT which had a mean of 21.0 and standard deviation of 4.7 and Mary got a 1260 on the SAT which had a mean of 1016 and standard deviation of 111. Calculate each z-score and determine whose score is better.

     

     

  10. A certain teacher uses the formula SAT/10×(17/14) to convert SAT scores taken at age 14 to IQ. Assuming IQs are normally distributed with a mean of 100 and standard deviation of 15 and that SAT scores are also normally distributed with a mean of 1016, a standard deviation of 111, and otherwise range from 200 to 1600, calculate the z-score for both the SAT score of 1190 and the corresponding calculated IQ. Is the formula good?

     

     

  11. (Bonus) Consider shoe size as measured both in width and length. Suppose both are normally distributed variables with 10D the mean for men with a standard deviations of 1.0 size and 1.0 letter. How might we find the probability of a shoe size of 6EEEEE, where widths have interval measurement specified by ... AAA, AA, A, B, C, D, E, EE, EEE ...?

     

     

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