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STD Surveillance. The Centers for Disease Control and Prevention compiles reported cases and rates of diseases in United States cities and outlying areas. In a document titled Sexually Transmitted Disease Surveillance, the number of reported cases of all stages of syphilis is provided for cities, including Orlando, Florida, and Cincinnati, Ohio. Following is the number of reported cases of syphilis for those two cities over the years $2007-2011$.

a. Obtain the individual population means the number of cases for both cities.

b. Without doing any calculations, decide for which city the population standard deviation of the number of cases is smaller. Explain your answer.

c. Obtain the individual population standard deviations of the number of cases for both cities.

d. Are your answers to parts (b) and (c) consistent? Why or why not?

Gestation Periods of Humans. Gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans.

a. Find the standardized variable corresponding to$y$

b. What are the mean and standard deviation of the standardized variable?

c. Obtain the $z$-scores for gestation periods of $227$days and $315$days. Round your answers to two decimal places.

d. Interpret your answers in part (c).

c. Construct a graph similar to Fig. 3.20 on page 146 that shows your results from parts (b) and (c).

Suppose you buy a new car whose advertised mileage is 25 miles per gallon (mpg). After driving your car for several months, you find that its mileage is 21.4mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for all cars of the model you bought is 1.15 mpg.

Part (a): Find the z-score for the gas mileage of your car, assuming the advertised claim is correct.

Part (b): Does it appear that your car is getting unusually low gas mileage?

A company produces cans of stewed tomatoes with an advertised weight of 14oz. The standard deviation of the weights is known to be 0.4oz. A quality - control engineer selects a can of stewed tomatoes at random and finds its net weight to be 17.28oz.

Part (a): Estimate the relative standing of that can of stewed tomatoes, assuming the true mean weight is 14oz. Use the z-score and Chebyshev's rule.

Part (b): Does the quality - control engineer have reason to suspect that the true mean weight of all cans of stewed tomatoes being produced is not 14oz? Explain your answer.

Copperhead and Tiger Snakes. S. Fearn et al. compare two types of snakes in the article 鈥淏ody Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania鈥� (Australian Journal of Zoology, Vol. 60, No. 3, pp. 159-165). Tiger snakes and lowland copperheads are both large snakes confined to the cooler parts of Tasmania. The weights of the male lowland copperhead in Tasmania have a mean of 812.07 g and a standard deviation of 330.24 g; the weights of the male tiger snake in Tasmania have a mean of 743.65 g and a standard deviation of 336.36 g.
a. Determine the z-scores for both a male lowland copperhead snake and a male tiger snake whose weights are 850 g.
b. Under what conditions would it be reasonable to use z-scores to compare the relative standings of the weights of the two snakes?
c. Assuming that a comparison using z-scores is legitimate, relative to the other snakes of its type, which snake is heavier?

Find the

a. Mean b. median c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations.

Daily Motorcycle Accidents. The Scottish Executive, Analy. tical Services Division Transport Statistics, compiles data on motor cycle accidents. During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built-up roads and non-built-up roads and resulted in the following data .

a. Find the mean and median of the number of accidents for built-up roads.

True of False: The mean, median and mode can all be used with quantitative data. Explain your answer.

a) Determine the mode of the data.
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer.

Medical School Faculty. The Association of American Medical College (AAMC) in a compiles data on medical school facility and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year.

Consider the data set: $1,2,3,4,5,6,7,8,9$.

a) Obtain the mean and median of the data.

b) Replace the $9$in the data set by $99$and again compare the mean and median. Decide which measure of the center works better here and explain your answer.

c) For the data set in part b) the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result.

Outliers and trimmed means. Some data sets contain outliers, observation that fall well outside the overall pattern of the data(We discuss outliers in more detail in section 3.4) Suppose, for instance that you are interested in the ability o high school algebra student to compute square roots. You decide to give a square root exam to 10 of these students Unfortunately, one of the student had a fight with his girlfriend and cannot concentrate he gets a 0. The 10 score are displayed in increasing order in the following table. The score of 0 is an outlier.

Statisticians have a systematic method for avoiding extreme observation and outliers when they calculated means. They compute trimmed means, in which high and low observation are deleted or "trimmed off" before the mean is calculated . For instance, to compute the 10% trimmed mean of the test score data. we first delete both the bottom 10% and the top 10% of the ordered data. that is,0 and 80. Then we calculated the mean of the remaining data. Thus the10% trimmed mean of the test score data is

The following table displays a set of score for a 40 question algebra final

Part (a) Do any the score look like outliers?

Part (b) Compute the usual mean of the data.

Part (c) Compute the 5% trimmed mean of the data.

Part (d) Compute the 10% trimmed mean of the data.
Part (e) Compare the means you obtained in parts (b) (d) which of the three provides the best measure of center for the data?