Review Chapter 3 Name

1. 
   The overall batting average of all major-league baseball hitters in recent years (1970 – 2008) has followed a roughly normal distribution with a mean of .261 and standard deviation .035.
   

(b) What percent of hitters bat .331 or higher? (Sketch a normal curve to illustrate and use the 68-95-99.7 rule.)

(c) In 2008, the batting leaders were Chipper Jones of the National League Atlanta Braves with a batting average of .364 and Joe Mauer of the American League Minnesota Twins, whose average was .328. When compared to the entire league, it is clear that Jones’ batting average was higher than Mauer’s, but what about their standing within their respective leagues? Below are the summary statistics for the 2008 top batting averages in each league.

League	Mean	Standard deviation (approx)
American (68 players)	.274	.042
National (72 players)	.279	.026

What are the standard scores for Mauer and Jones within their own league? Who had the more outstanding year? Explain your reasoning.

1. 
   Approximately what proportion of adult males are taller than 71.9 inches? (Draw a normal density curve and use the 68-95-99.7 rule).
   

2. 
   Find the approximate proportion of adult males who are taller than 68 inches using the standard normal distribution and Table A. Report Table A values to 4 decimal places.
   

3. 
   What percent of adult females are between 60 inches and 66 inches tall?
   

4. 
   If there were 4000 females in the sample, about how many would we expect to be between 60 and 66 inches tall?
   

5. 
   Find the height that corresponds to the 70^th percentile of the height distribution for adult males.
   

6. 
   To what percentile in the adult female height distribution would your answer in part (e) correspond?
   

1. 
   If the company sold 250,000 of these tires this year, approximately how many would it expect to have to replace under the warranty conditions?
   

1. 
   Draw an appropriate density curve for summarizing the histogram above. How would you describe the shape of this density curve?
   

2. 
   Where would the mean and median be located on the density curve you drew in part (a)? Draw in their approximate locations.
   

3. 
   Based on the histogram, what is the approximate percentile of the opening price of $35?
   

4. 
   Based on the histogram, what is the approximate opening stock price which represents the 97^th percentile?
   

5. 
   The mean and standard deviation of the distribution of the opening day price for Apple stock is $64.94 and $49.50, respectively. What is the z-score for the opening day price of $107.40?
   

5. Syracuse, New York is the snowiest metropolitan area in the United States. Based on 59 years of data from the National Weather Center, the mean annual snowfall is 118.5 inches with a standard deviation of 33.5 inches. The annual snowfall in Syracuse follows a roughly normal distribution.

(a) Sketch a normal curve to illustrate the annul snowfall in Syracuse. Be sure to mark the mean and the points that determine one, two, and three standard deviations away from the mean.

(b) Use the 68-95.99.7 rule to estimate the percent of years where the annual snowfall was between 85 inches and 185.5 inches. Illustrate your method clearly.