27)A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.5 years, and standard deviation of 1.6 years. The 10% of items with the shortest lifespan will last less than how many years?

28)A particular fruit's weights are normally distributed, with a mean of 599 grams and a standard deviation of 31 grams. The heaviest 16% of fruits weigh more than how many grams?

29)The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 39 liters, and standard deviation of 9.8 liters. A) What is the probability that daily production is less than 41.8 liters? Use technology (not tables) to get your probability.

B) What is the probability that daily production is more than 24.9 liters? Use technology (not tables) to get your probability.

30)The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 35 liters, and standard deviation of 2.3 liters. A) What is the probability that daily production is between 38 and 40.7 liters? Do not round until you get your your final answer.

31)An electronic product takes an average of 7 hours to move through an assembly line. If the standard deviation of 0.8 hours, what is the probability that an item will take between 6.3 and 6.4 hours to move through the assembly line? Assume the population is normally distributed. Do not round until you get your your final answer.

32)Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean = 92.12 mph and a standard deviation of = 2.43 mph. Compute thez-score of pitch with speed 85.2 mph. (Round your answer to 2 decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 93.4 mph and 95.4 mph? (Express your answer as a decimal, not a percent, and round to 4 decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds above 95.4 mph? (Express your answer as a decimal, not a percent, and round to 4 decimal places.) A baseball fan wishes to identify the four-seam fastballs among the slowest 7% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 7%? (Round your answer to the nearest 0.1 mph.)

33)Kyle finds that in a suburb of Nashville, the weekly salary for a basic office worker has a normal distribution with a mean of $558 and a standard deviation of $84. The highest 18% of weekly earners are not eligible for a raise (so the top 18% of all the salaries can't get a raise). What weekly salary does a worker have to earn to make them not eligible for a raise?