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STATISTICS 101 - Homework 6 Due Friday, March 8, 2002 • Homework is due by 5:00 PM on the due date in my oﬃce. You can always hand in your homework at the end of lecture on Friday. • You may talk with others about the homework problems but please write your solutions up independently. Please answer homework questions in complete sentences. Make sure to staple the pages of your assignment together. Be sure to indicate your lab section on your paper. • You will have an opportunity to get help on homework during lab. Reading: Feb. 22 Mar. 1 - Feb. 27 - March 6 Section 1.3 Section 4.3 Assignment: 1. Read pages 210-218 and answer exercise 4.2 in the text. 2. Read pages 46-64 and answer exercises 1.62, 1.66, 1.68 in the text. 3. Freshmen entering college in the Fall of 1995 had a mean ACT Composite score of 21. The standard deviation was 5. Assuming that ACT Composite scores are normally distributed, use the 68-95-99.7 rule to answer the following questions. (a) What percentage of entering Freshmen in Fall 1995 had an ACT Composite score between 16 and 26? (b) What percentage of entering Freshmen in Fall 1995 had an ACT Composite score below 11? (c) The Admissions Oﬃce wishes to set high standards but does not wish to reject to large a percentage of applicants based on ACT Composite score. What should the minimum ACT Composite score be so that at most 16% of students would fall below this minimum? (d) What ACT Composite scores would put someone in the top 0.15% of the entering Freshman class in Fall of 1995? 4. Data was collected on the body temperature (o F ) for a sample of 65 males. The data are summarized below in a frequency table. Body 96.0 96.5 97.0 97.5 98.0 98.5 99.0 99.5 100.0 100.5 Temperature ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < ≤ T emp < 1 (o F ) 96.5 97.0 97.5 98.0 98.5 99.0 99.5 100.0 100.5 101.0 Count 0 1 5 10 17 16 10 4 1 1 (a) Construct a histogram for body temperatures for the sample of 65 males. Describe the shape of the histogram. Where is the approximate center of the histogram? (b) What is the relative frequency for: i. a temperature less than 98.0? ii. a temperature greater than or equal to 99.5? iii. a temperature greater than or equal to 97.0 but less than 100.0? (c) It seems reasonable to model the distribution of body temperature for the male population as a normal distribution. Assuming this normal (bell) shape with a population mean, µ = 98.5 and a population standard deviation, σ = 0.75, what is the probability for: i. a temperature less than 98.0? ii. a temperature greater than or equal to 99.5? iii. a temperature greater than or equal to 97.0 but less than 100.0? (d) How close are the normal probabilities computed in (c) to the relative frequencies in (b)? What does this say about the appropriateness of the normal model for body temperatures? (e) From the frequency table can you determine the relative frequency for a male body temperature greater than or equal to 98.6? (f) Using the normal model, compute the probability that a male body temperature is greater than or equal to 98.6. (g) Using the normal model, what is the temperature such that only 1% of males would have temperatures greater than or equal to this value? 2