Module 5 Homework: Density Curves and Normal Approximation

Homework Exercises:

Part I

There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores is approximately Normal with mean µ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The distribution of SAT scores is approximately Normal with mean µ = 1498 and standard deviation σ = 316.

1. Jessica scores 2020 on the SAT. Ashley scores 29 on the ACT. Assuming that both tests measure the same thing, who has the higher score ? Hint: Compute the z-scores for both Jessica and Ashley. Show your calculations . (3 pts)
2. Jorge scores 1990 on the SAT. Assuming that both the SAT and ACT measure the same thing, what score on the ACT is equivalent to Jorge’s SAT score? Use the NORMDIST and NORMINV functions in Excel as appropriate (see the Lecture notes). Show the values entered in your use of the NORMDIST and NORMINV functions. Clearly label your work. (3 pts)
3. What ACT score makes up the top 10% of all ACT scores? Hint: asking for the top 10% is equivalent to asking to find scores to the left of the 90 ^th percentile. So, to answer this question: Use Table A in the back of your textbook ("Standard Normal Probabilities Table") to find the proportion closest to 0.90 (1-0.10=0.90). From that proportion, locate the z-score. Solve for X using the z-score obtained: x=µ + z σ Show your calculations. Clearly label your work. (3 pts)
4. Check your answer by using the NORMDIST function in Excel. Show your NORMDIST function with the parameters you used to derive answer. (2 pts)
5. What is the range of SAT scores earned by approximately 95% of students? Hint: Use the 68-95-99.7 rule. Show your calculations. Don’t forget to answer the question asked. (2 pts)
6. What students SAT scores would be considered outliers? Use the 68-95-99.7 rule. Show your calculations. (2 pts)

Part II

Conventional wisdom suggests that women are more talkative than men. One study designed to examine this stereotype collected data on the speech of 42 women and 37 men in the United States. In the dataset talk.xls (posted in the D2L dropbox for this homework assignment), the variable of interest is "WordsPerDay." Completing the following tasks, assess whether the data distribution for this variable appears to be Normal. (Don’t worry about splitting by gender; just assess the normality of the WordsPerDay variable.)

1. Create a normal probability (‘Normal Q-Q) plot in SPSS. (See Lecture notes) (2 pts)
   [copy and paste your graph here]
2. Create a histogram with the density curve drawn. (GraphsLegacy Dialogs Histogram. Choose WordsPerDay as the Variable. Click the checkbox "Display Normal Curve". Click "Ok") (2 pts)
   [copy and paste your graph here]
3. In your opinion, do these data appear to be "approximately" normally distributed? Briefly justify your answer by referencing the above graphs. (Answers will vary based on students’ perceptions. The key is to justify ‘your’ answer.) (1 pt)

Price: $12.85

Solution: The downloadable solution consists of 5 pages, 785 words and 2 charts.
Deliverable: Word Document