UMUC Statistics Quiz 3 #2b

1. (5 points) Use the Z-score applet to do the following problem. Provide a screen shot for

your answers.

http://davidmlane.com/hyperstat/z_table.html

The average flyball in baseball travels 380 ft from home plate. The standard deviation is

10 feet. Assume that the distance distribution follows the Bell curve. Provide screen shots

of your answers.

a. What percent of flyballs which travel a distance between 390 and 400 feet? (use

“Area from a value”)

b. If a flyball is in the 45 th percentile, how far did the ball travel? (use “Value from an

area”)

c. What is the z-score of a flyball that travels 375 feet? (z = )

2. (10 points) Given a sample size of n = 225. Let the variance of the population be σ 2 =

8.41. Let the mean of the sample be xbar = 12. Construct a 99% confidence interval for µ,

the mean of the population, using this data and the central limit theorem.

a. What is the standard deviation (σ) of the population?

b. What is the standard deviation of the mean xbar of sample size n, i.e. what is σ xbar , in

terms of σ and n?

c. Is this a one-sided or two-sided problem?

d. What value of z should be used in computing k, the margin of error, where

z = k/σ xbar = k/[σ/ ]?

e. What is k?

f. Write the 99% confidence interval for µ based on xbar and k,

(xbar – k) < µ < (xbar + k)

g. Using the Z-score applet “Area from a value”. Let the Mean = 12, and SD = σ xbar .

Choose “Between (xbar -k) and (xbar + k)” using xbar = 12 and your computed value

of k. Hit “Recalculate”. Does the probability approximately equal 0.99? (yes or no).

Include a screen shot of your answer.

3. (10 points) A very large school system claims that it has a 85% graduation rate. A sample

of 900 seniors found that 725 received their high school diploma. Construct a 90%

proportion confidence interval based on this data and determine whether the data supports

the 85% statement.

Start by using the binomial distribution. = n σ =

a. What is n?

b. What is ?

c. What is ?

d. What is ?

e. What is p? (Note: p is based on our belief about the population. is based on the

sample.)

f. What is σ?

g. Let σ p = sqrt(). What is σ p ?

h. We want to make a 90% confidence interval by using the formula

z = k/σ p

Should we use a 1 tail or 2 tail z-score?

i. What value of z corresponds to the desired 90% confidence interval?

j. What is k?

k. Construct the confidence interval

( – k) < p true < ( + k)

l. Is your confidence interval consistent with the belief that 85% of high school students

graduate? (yes or no, and explain your answer using your computed confidence

interval).