A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.8 years, and standard deviation of 2.1 years.lf you randomly purchase one item, what is the probability it will last longer than 11 years? Round your answer to three decimal places Suppose paper bag width measurements are approximately normally distributed with a mean of 20.1 inches, and standard deviation of 2.3 inches. What is the probability that the height of a randomly chosen paper bag is between 14.85 and 22.25 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 0.912 g and a standard deviation of 0.286 g. Find the probability of randomly selecting a cigarette with 0.34 g of nicotine or less. Give your answer as a number accurate to 3 decimal places. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.6 years, and standard deviation of 1.3 years. The 5% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place. A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1095 and a standard deviation of 203. Scores on the ACT test are normally distributed with a mean of 19.5 and a standard deviation of 4.5. It is assumed that the two tests measure the same aptitude. but use different scales. If a student gets an SAT score that is the 67- percentile, find the actual SAT score. Round to a whole number For a standard normal distribution, find: P(2 > 0.05) Express the probability as a decimal rounded to 4 decimal places. A particular fruit's weights are normally distributed, with a mean of 478 grams and a standard deviation of 9 grams. If you pick one fruit at random, what is the probability that it will weigh between 447 grams and 457 grams? | The heaviest 15% of fruits weigh more than how many grams? Here is the setup for a non-traditional dice game: You roll a die and if the die is a 6 you win $100. The game costs $5 to play and you decide to play the game until you win the $100. Each time you roll a die you pay $5, and if it is not a 6, you lose your 55. How much money should you expect to spend on this game? i The number of chocolate chips in a cholate chip cookie has a bell-shaped distribution. This distribution has a mean of 12 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage cookies numbering between 4 and 24? (Round percent number to 2 decimal places.) ans = % The heights of adult men in America are normally distributed, with a mean of 69.9 inches and a standard deviation of 2.71 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.9 inches and a standard deviation of 2.61 inches. a} If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)? b) If a woman is 5 feet 6 inches tall, what is her z-score (to two decimal places]? c) Who is relatively taller? O The 6 foot 2 inch American man 0 The 5 foot 6 inch American woman A large company knows that replacement times for the calculators it produces are normally distributed with a mean of 2.6 years and a standard deviation of 0.4 years. Find the probability that a randomly selected calculators will have a replacement time less than 1.3 years? Write your answer accurate to 4 decimal places. A large company knows that replacement times for the calculators it produces are normally distributed with a mean of 10 years and a standard deviation of 1.3 years. If the company wants to provide a warranty so that only 2.5% of the calculators will be replaced before the warranty expires, what is the time length of the warranty? (Write your answer as a number accurate to 1 decimal place.) L J g.) Is 6 an unusually high number of left-handed people in a group of 16? O Yes because P(X>=6)>0.05 0 Yes because P(X0.05 O No because P(X>=6)0.05 0 Yes because P(X=6) >0.05 O Yes because P(X>=6)=6)>0.05 O No because P(X=6) >0.05 0 Yes because P(X=6) 5.3 or X