Download Chapter 5 Technology Exercise

Chapter 5 Technology
Name : <enter name here>
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
z = - 1.24
z = 0.84
z = 2.98
area to left
area to right
twice smaller area
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
Normal
16
Normal
16
Uniform
16
Uniform
16
Skewed
8.08
Skewed
8.08
Pop SD
5
5
9.52
9.52
6.22
6.22
N
2
5
10
16
20
25
Samp Mean
Samp SD
Shape
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
99% confidence level
95% confidence level
n = 10
n = 15
n = 20
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
http://www.harrisinteractive.com/harris_poll/index.asp?PID=640
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%?