Chapter 6: Q6.3 (page 259)
Variable having density curve - has percentage of observations lie within a range equal to corresponding area between those values in its density curve.
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In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.
Sampling Distribution of the Sample Median
a. Find the value of the population median.
b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table 6-3. (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)
c. Find the mean of the sampling distribution of the sample median. d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not?
In Exercises 11–14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in Coca-Cola Zero, Diet Pepsi, Dr Pepper, and Mellow Yello Zero.
Assume that random samples of size n = 2 are selected with replacement.
Sampling Distribution of the Range Repeat Exercise 11 using ranges instead of means.
Durations of PregnanciesThe lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
a. In a letter to “Dear Abby,” a wife claimed to have given birth 308 days after a brief visit fromher husband, who was working in another country. Find the probability of a pregnancy lasting308 days or longer. What does the result suggest?
b. If we stipulate that a baby is prematureif the duration of pregnancy is in the lowest 3%,find the duration that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administrators in planning for that care.
Sampling with Replacement The Orangetown Medical Research Center randomly selects 100 births in the United States each day, and the proportion of boys is recorded for each sample.
a. Do you think the births are randomly selected with replacement or without replacement?
b. Give two reasons why statistical methods tend to be based on the assumption that sampling is conducted with replacement, instead of without replacement.
Standard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers
to four decimal places.
Between -2.00 and 2.00.
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