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**1. Platelet Counts Distribution:**

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.7 and a standard deviation of 62.6. All units are in 1000 cells/L.

**a.** What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.9 and 441.5?

Approximately ___% of women in this group have platelet counts within 3 standard deviations of the mean, or between 65.9 and 441.5. (Type an integer or a decimal. Do not round.)

**b.** What is the approximate percentage of women with platelet counts between 128.5 and 378.9?

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**2. Body Temperatures of Healthy Adults:**

According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.08°F and a standard deviation of 0.66°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean?

What are the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean?

At least ___% of healthy adults have body temperatures within 2 standard deviations of 98.08°F. (Round to the nearest percent as needed.)

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**3. Cigarettes Population Analysis:**

Let a population consist of the values 11 cigarettes, 12 cigarettes, and 22 cigarettes smoked in a day.

Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?

Calculate the mean absolute deviation for each possible sample of size 2 from the population. (Type integers or decimals rounded to one decimal place as needed.)

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**4. Parking Meter Collections:**

Listed below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees?

Find the coefficient of variation for each of the two samples, then compare the variation.

The coefficient of variation for the amount collected by the security service company is __%. (Round to one decimal place as needed.)

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**5. Pulse Rates Analysis:**

Listed below are pulse rates (beats per minute) from samples of adult males and females. Does there appear to be a difference?

Find the coefficient of variation for each of the two samples; then compare the variation.

The coefficient of variation for the male pulse rates is __%. (Type an integer or decimal rounded to one decimal place as needed.)

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**6. Bank Waiting Times:**

Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below.

Find the coefficient of variation for each of the two sets of data, then compare the variation.

The coefficient of variation for the waiting times at Bank A is __%. (Round to one decimal place as needed.)

Answer :

Final answer:

The empirical rule states that for data with a bell-shaped distribution, a certain percentage of the data falls within a certain number of standard deviations from the mean. Using this rule, we can find the percentage of women with platelet counts within a given range. For part a, the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.9 and 441.5, is greater than 99%. For part b, we can calculate the z-scores for the given platelet count range and use them to find the corresponding percentage.

Explanation:

The empirical rule states that for data with a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and more than 99% falls within three standard deviations.

For part a, the platelet counts between 65.9 and 441.5 are within 3 standard deviations of the mean. Using the empirical rule, approximately 99% (more than 99%) of women have platelet counts within 3 standard deviations of the mean.

For part b, to find the percentage of women with platelet counts between 128.5 and 378.9, we need to calculate the z-scores for these values:

Z-score for 128.5: (128.5 - 253.7) / 62.6 = -2. milliseconds

Learn more about Descriptive Statistics here:

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