Week 7 Quiz Notes

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Math 221
Quiz Review for Weeks 5 and 6

1. Find the area under the standard normal curve between z = 1.6 and z = 2.6. First we look for the area of both by doing “2nd ,Vars, NORMALCDF” and inputting “-1000, “Z,” 0, 1 then find the difference between both.

2. A business wants to estimate the true mean annual income of its customers. It randomly samples 220 of its customers. The mean annual income was $61,400 with a standard deviation of $2,200. Find a 95% confidence interval for the true mean annual income of the business’ customers.
First we find E by doing Zc(standard deviation/square root of number of trials.) Now we add and subtract that number from the mean income to find both endpoints. The Zc of 95% is 1.96 so we would do
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11. What z-scores would be used to create an 89% confidence interval?

12. A soccer ball manufacturer wants to estimate the mean circumference of mini-soccer balls within .12 inch. Assume that the population of circumferences is normally distributed.
Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population's standard deviation is .2 inches.
13. Find the area under the standard normal curve to the left of z = -1.25.
14. True or False. In the standard normal distribution the standard deviation is always exactly 0.
15. Compute the population mean margin of error for a 90% confidence interval when sigma is 7 and the sample size is 36.
16. The area under a normal curve with mu = 35 and sigma = 7 is 0, 1, or 2?
17. If John gets an 90 on a physics test where the mean is 85 and the standard deviation is 3, where does he stand in relation to his classmates? (he is in the top 5%, he is in the top 10%, he is in the bottom 5%, or bottom 1%)
18. Find P(12 < x < 23) when mu = 19 and sigma = 6. Write your steps in probability notation.
19. In a normal distribution with mu = 34 and sigma = 5 what number corresponds to z = -4?
20. Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.
21. Interpret a 93% confidence interval of (7.46, 12.84) for a population mean.
22. The

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