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3. A bin contains 78 light bulbs, 8 of which are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all of the bulbs selected are good. Round to three decimal places as needed.
4. Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $5000. What is your expected value?
6. Of the 9394 registered voters in one town, 4602 are women. Among a sample of 550 of the registered voters from this town, 261 are women. Find the population proportion of registered voters who are women, rounded to two decimal places as needed.
7. The distribution of sample means for a group of test scores for samples of 100 scores is normal with a mean of 64.7 and a standard deviation of 1.6. Suppose you take a sample of 100 test scores and find that the mean is 67.5. How many standard deviations is the sample mean from the mean of the distribution of sample means? Round to the nearest tenth as needed.
9. If P(A)=1/5, find P(A).
11. A medical researcher wishes to estimate the mean systolic blood pressure of heart surgery patients the day following surgery. She desires a margin of error of 1.7 mmHg. Past studies suggest that a population standard deviation of 41 mmHg is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
12. A medical researcher wishes to estimate what proportion of babies born at a particular hospital are born by Caesarean section. In a random sample of 81 births at the hospital, 25% were Caesarean sections. Find the margin of error for the 95% confidence interval of the population proportion. Round to four decimal places.
13. Use the relative frequency method to estimate the probability. Round to three decimal places. A pollingfirm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 0=FOR, 1=AGAINST. If the referendum were held today, estimate the probability that it would pass.
0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0
14. For several customers at the local coffee shop, the scatter diagram compares the cost of their coffee (y) and the number of cups of coffee they drink (x). State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables. If there is a correlation, state whether it is most likely due to coincidence, a common underlying cause, or a direct cause.
15. A sample of 49 statistics students at a small college had a mean mathematics ACT score of 24 with a standard deviation of 6. Find the 95% confidence interval. Round to two decimal places.