• A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.1 years, and standard deviation of 2.9 years. If you randomly purchase one item, what is the probability it will last longer than 19 years? Round to three decimal.
• In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55 inches, and standard deviation of 6.7 inches. What is the probability that the height of a randomly chosen child is between 50.95 and 66.85 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
• The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.939 g and a standard deviation of 0.323 g. Find the probability of randomly selecting a cigarette with 0.519 g of nicotine or less. P(X < 0.519 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.
• Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0C and a standard deviation of 1.00C. A single thermometer is randomly selected and tested. Find P₅₃, the 53-percentile. This is the temperature reading separating the bottom 53% from the top 47%.