# mathematics

NYIT TAKE-HOME QUIZ ON NORMAL DISTRIBUTION Due Friday, March 13 by 6pm EST by posting in the applicable Blackboard assessment tab – e-mail, hand submittals cannot be accepted – shortly after 6pm, I will post solution for your review and revision if like to enhance grade. 1. The distribution of the annual incomes of foremen at the Marvin Window Company approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68% of the incomes lie between what two incomes? 2. Which of the following is true in a normal distribution? A. The mean equals zero. B. The mode and the third quartile are equal. C. The mean divides the distribution into two equal areas. D. The area under the curve is 0.68. 3. Tables of normal distribution probabilities are found in many statistics books. These probabilities are calculated from a normal distribution with ___________. A. A mean of 1 and a standard deviation of 1 B. A mean of 100 and a standard deviation of 15 C. A mean of 0 and a standard deviation of 15 D. A mean of 0 and a standard deviation of 1 4. Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true? A. The locations of the distributions are different. B. The distributions are from two different families of distributions. C. The dispersions of the distributions are different. D. The dispersions of the distributions are the same. 5. A normally distributed random variable has _________. A. Any value between -∞ and + ∞. B. Discrete values. C. Any value between specified minimum and maximum values. D. Only two values, success and failure. 6. The total area of a normal probability distribution is _______. A. Between -3.0 and 3.0 B. 1.00 C. Dependent on a value of “z” D. Approximated by the binomial distribution 7. In an illustration of a normal probability distribution, a shaded area represents _______. A. A permutation B. A combination C. A probability D. A standard deviation 8. The standard normal probability distribution is unique because it has _________. A. A mean of 1 and any standard deviation B. Any mean and a standard deviation of 1 C. A mean of 0 and any standard deviation D. A mean of 0 and a standard deviation of 1 9. The weekly mean income of a group of carpenters is $1,000 and the standard deviation of this group is $100. The distribution is normal. What percent of the carpenters have an income of $925 or less? 10. A candy bar is normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What percent of the candy bars weigh 860 grams or less? 11. What is a normal distribution with a mean of 0 and a standard deviation of 1 called? A. Frequency distribution B. Z-score C. Standard normal distribution D. Binomial probability distribution 12. The mean weight of a watermelon plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of 200 watermelons, how many weighed between 13 and 16 pounds? 13. The Marvin Window Company estimated that the distribution of the time for two construction workers to install 50 custom window sets is normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of 50 window sets take between 32 and 34 hours to erect? .