Practice Quiz Week 7 Statistics Essay

1999 words - 8 pages

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.

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.

3. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 120. Find the z-score corresponding to this value.

4. Two high school students took equivalent language tests, one in German and one in French. The ...view middle of the document...

The engineer crashes 24 Corvettes and finds the mean damage is $11,500 with a standard deviation of $2,700. Find a 98% confidence interval for the true mean cost to repair this type of car.

9. A competency test has scores with a mean of 80 and a standard deviation of 10. A histogram of the data shows that the distribution is normal. Use the Empirical Rule to find the percentage of scores between 70 and 90.

10. An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor wants to be within 11% of the true proportion when using a 90% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

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 area to the left of "z" is .5438. What z score corresponds to this area?
23. What is the critical z-value that corresponds to a confidence level of 86%?


Answers

1. Using the Table of Areas, a “between” problem always means that we subtract the area found in the table corresponding to the smaller z-score from the area found in the table corresponding to the larger z-score. The area for 1.6 is .9452 and the area for 2.6 is .9953 so .9953 - .9332 = .0501
In probability notation we would write
P(1.6 < z < 2.6)
= P(z < 2.6) - P(z < 1.6)
=.9953 - .9452
= .0501

2. The population standard deviation is unknown and the sample size is 220. Thus, since the sample size is greater than 30, this confidence interval will use a z-value. For a...

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