Problem 1
If scores are normally distributed with a mean of 35 and a standard deviation of \(10,\) what percent of the scores is: a. greater than 34 ? b. smaller than \(42 ?\) c. between 28 and \(34 ?\)
Problem 2
What are the mean and standard deviation of the standard normal distribution? (b) What would be the mean and standard deviation of a distribution created by multiplying the standard normal distribution by 8 and then adding \(75 ?\)
Problem 3
The normal distribution is defined by two parameters. What are they?
Problem 4
What proportion of a normal distribution is within one standard deviation of the mean? (b) What proportion is more than 2.0 standard deviations from the mean? (c) What proportion is between 1.25 and 2.1 standard deviations above the mean?
Problem 5
A test is normally distributed with a mean of 70 and a standard deviation of 8 . (a) What score would be needed to be in the 85 th percentile? (b) What score would be needed to be in the 22 nd percentile?
Problem 6
Assume a normal distribution with a mean of 70 and a standard deviation of 12 . What limits would include the middle \(65 \%\) of the cases?
Problem 7
A normal distribution has a mean of 20 and a standard deviation of \(4 .\) Find the \(Z\) scores for the following numbers: (a) 28 (b) 18 (c) 10 (d) 23.
Problem 8
Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of \(71 \mathrm{mph}\) and a standard deviation of \(8 \mathrm{mph}\). a. The current speed limit is \(65 \mathrm{mph}\). What is the proportion of vehicles less than or equal to the speed limit? b. What proportion of the vehicles would be going less than \(50 \mathrm{mph}\) ? c. A new speed limit will be initiated such that approximately \(10 \%\) of vehicles will be over the speed limit. What is the new speed limit based on this criterion? d. In what way do you think the actual distribution of speeds differs from a normal distribution?
Problem 9
A variable is normally distributed with a mean of 120 and a standard deviation of \(5 .\) One score is randomly sampled. What is the probability it is above \(127 ?\)
Problem 11
A group of students at a school takes a history test. The distribution is normal with a mean of \(25,\) and a standard deviation of \(4 .\) (a) Everyone who scores in the top \(30 \%\) of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate? (b) The top \(5 \%\) of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?
