Chapter 2 Technology
Chapter 5 Technology Name :
1. Assume a standard normal distribution with a mean of 0 and a standard deviation of 1. Find the following areas for each of the z-scores. Give values to 6 decimal places.
|z-score |area to left |area to right |twice smaller area |
|z = - 1.24 | | | |
|z = 0.84 | | | |
|z = 2.98 | | | |
2. Assume a standard normal distribution. Find the z-score that has the area given. Give answers with at least five decimal places.
a. Area to left = 0.287324, z =
b. Area to right = 0.872316, z =
c. Area between -z and z is 0.452684, z =
3. The English scores for those students in Illinois who took the ACT exam in 2004 are normally distributed with a mean of 19.7 and a standard deviation of 6.3.
a. Sally scored a 26 on the English portion of the ACT exam. What percent of the students did better than Sally?
b. A student must score above the 40th percentile to be eligible for ENGL 101, what raw score corresponds to the 40th percentile?
4. Use the sampling distribution applet from the statistical demonstrations page on the website to see how the mean of a sample behaves.
|Distribution |Pop Mean |Pop SD |N |Samp Mean |Samp SD |Shape |
|Normal |16 |5 |2 | | | |
|Normal |16 |5 |5 | | | |
|Uniform |16 |9.52 |10 | | | |
|Uniform |16 |9.52 |16 | | | |
|Skewed |8.08 |6.22 |20 | | | |
|Skewed |8.08 |6.22 |25 | | | |
a. In each case, how does the mean of the sample means compare to the mean of the population?
b. How can you find the standard deviation of the sample means if you know the population standard deviation and the sample size?
c. What can you say about the effect the sample size has on the shape of the sampling distribution of the sample means (you may need to try the skewed distribution with all of the sample sizes to notice the pattern)
5. Use the confidence interval simulation applet from the statistical demonstrations page on the website to see what a confidence interval really means. Run the simulation at least 50 times (each sample contains 100 trials) for each of the sample sizes (10, 15, and 20) being sure to hit clear when you switch sample sizes.
a. Complete the table by recording the proportion of confidence intervals that contain the actual mean of 50.
|proportion contained |n = 10 |n = 15 |n = 20 |
|99% confidence level | | | |
|95% confidence level | | | |
b. Explain how the confidence level relates to the process of finding a confidence interval (read page 270 in your book).
6. Read the Harris Poll® #16, February 16, 2006, at
a. According to a Harris Poll, what percent of U.S. adults say the country has pretty seriously gotten off on the wrong track?
b. What is the sample size for this survey?
c. Find a 95% confidence interval for the true proportion of U.S. adults who feel the country is on the wrong track.
d. The article claims that the percent has risen from 54% in January. Does your confidence interval contain 54%?
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