• Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 5.9-in and a standard deviation of 1.1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.4% or largest 2.4%. What is the minimum head breadth that will fit the clientele? min = What is the maximum head breadth that will fit the clientele? min = Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
• A manufacturer knows that their items have a normally distributed length, with a mean of 10.3 inches, and standard deviation of 1.5 inches. If one item is chosen at random, what is the probability that it is less than 8.6 inches long?
• A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.5 years, and standard deviation of 2.4 years. If you randomly purchase one item, what is the probability it will last longer than 18 years?
• A particular fruit's weights are normally distributed, with a mean of 537 grams and a standard deviation of 30 grams. If you pick one fruit at random, what is the probability that it will weigh between 444 grams and 467 grams
• A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.5 years, and standard deviation of 2.2 years. The 2% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place.