1. The scores on a standardized test for high school students are normally distributed with a population mean of 500 and a population standard deviation of 100. Use the empirical rule (0LI refers to this as the standard deviation rule.). Make sure you provide graphs for each part as specified in the assignment directions (page 1 of this document).
a. What is the probability that a student has a score greater than 600?
b. What is the probability a student has a score between 300 and 600?
c. What is the probability a student has a score between 200 and 400?
d. What is the probability a student has a score less than 300?
e. What score would a student need to get on this test to place at the 97.5th percentile? This is a score such that our student scores higher than 97.5% (or .975 in probability terms) of students taking the exam?
2. In a particular market, 40% of people have seen and can recall a particular commercial. A random sample of 10 is selected from the population.
a. Report the probability distribution in the space below; i.e., list all possible values of x (the number of people who have seen and can recall the commercial) and the probability for each value.
b. What is the probability that at least 3 have seen and can recall a particular commercial?
c. What is the probability that more than 7 have seen and can recall a particular commercial?
d. What is the probability that less than 2 have seen and can recall a particular commercial?
e. Based on your answer to part d, what would you conclude if less than 2 have seen and can recall a particular commercial? Explain. [Interpret using .05 as a “cutoff.”]
3. The distribution of driving speeds on rural highways in Arkansas is normally distributed with a population mean of 48 miles per hour and a population standard deviation of 6 miles per hour. Use the empirical rule (0LI refers to this as the standard deviation rule.). Make sure you provide graphs for each part as specified in the assignment directions (page 1 of this document).
a. What is the likelihood that a particular car will be traveling over 60 miles per hour?
b. What is the likelihood that a particular car will be traveling under 30 miles per hour?
c. What is the likelihood that a particular car will be traveling between 54 and 60 miles per hour?
d. What is the likelihood that a particular car will be traveling between 42 and 60 miles per hour?
e. Find the 16th percentile.
4. According a Department of Education report, the probability of a student (entering freshmen) graduating from college in four years is 0.4. A random sample of six students (entering freshmen) is selected.
a. Write probability distribution in the space below (left hand side of table). Then draw a graph of the probability distribution (right hand side of table).
Probability Distribution
X p(x) Graph
b. In a random sample of six students (entering freshmen), what is the probability that none (zero) graduate from college in four years?
Probability (4 decimal places) = ____________
c. Based on the probability calculated in the preceding answer, what do you think about the claim made by Department of Education report? Explain. [Interpret using .05 as a “cutoff.”]
d. In a random sample of six students (entering freshmen), what is the probability that less than two graduate from college in four years?
Probability (4 decimal places) = ____________
e. Based on the probability calculated in the preceding answer, what do you think about the claim made by Department of Education report? Explain. [Interpret using .05 as a “cutoff.”]
5. What happens to the shape of the binomial distribution as the sample size gets larger? (One sentence should do it.)
6. What happens to the shape of the binomial distribution as the probability in the problem (often called the “probability of success”) gets closer to .5? (One sentence should do it.)
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will help you with the first problem.
1a-e. Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.
Squared deviations ___________ zero.
Answer A. are always greater than
B. are always greater than or equal to
C. are always less than
D. may be greater or less than