The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 61 ounces and a standard deviation of 11 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Use the Empirical Rule and sketch the distribution in order to answer these questions.
a) 99.7% of the widget weights lie between ____ and ______
b) What percentage of the widget weights lie between 50 and 94 ounces? ______ %
c) What percentage of the widget weights lie above 39 ?____ %
2.) The results of a common standardized test used in psychology research is designed so that the population mean is 170 and the standard deviation is 20. A subject earns a score of 210. What is the z-score for this raw score?
3. Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of -3.1 (to 2 decimal places)
4.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8 years, and standard deviation of 1.2 years.
If you randomly purchase one item, what is the probability it will last longer than 9 years?
Round answer to three decimal places
5.) The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.914 g and a standard deviation of 0.286 g. Find the probability of randomly selecting a cigarette with 0.657 g of nicotine or less.
P(X < 0.657 g) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
6.) In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.6 inches, and standard deviation of 4.3 inches.
What is the probability that the height of a randomly chosen child is between 43.15 and 48.25 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
Answer= (Round your answer to 3 decimal places.)