Problem 12
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?
Problem 13
True/false: For any normal distribution, the mean, median, and mode will be equal.
Problem 14
True/false: In a normal distribution, \(11.5 \%\) of scores are greater than \(\mathrm{Z}=1.2 .\)
Problem 16
True/false: The larger the \(\mathrm{n}\), the better the normal distribution approximates the binomial distribution.
Problem 17
True/false: A Z-score represents the number of standard deviations above or below the mean.
Problem 18
True/false: Abraham de Moivre, a consultant to gamblers, discovered the normal distribution when trying to approximate the binomial distribution to make his computations easier.
Problem 24
A set of test scores are normally distributed. Their mean is 100 and standard deviation is \(20 .\) These scores are converted to standard normal z scores. What would be the mean and median of this distribution? a. 0 b. 1 c. 50 d. 100
Problem 25
Suppose that weights of bags of potato chips coming from a factory follow a normal distribution with mean 12.8 ounces and standard deviation .6 ounces. If the manufacturer wants to keep the mean at 12.8 ounces but adjust the standard deviation so that only \(1 \%\) of the bags weigh less than 12 ounces, how small does he/she need to make that standard deviation?
Problem 28
Suppose that combined verbal and math SAT scores follow a normal distribution with mean 896 and standard deviation \(174 .\) Suppose further that Peter finds out that he scored in the top \(3 \%\) of SAT scores. Determine how high Peter's score must have been.
Problem 29
Heights of adult women in the United States are normally distributed with a population mean of \(\mu=63.5\) inches and a population standard deviation of \(\sigma=\) 2.5. A medical re- searcher is planning to select a large random sample of adult women to participate in a future study. What is the standard value, or z-value, for an adult woman who has a height of 68.5 inches?
