An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150lb and 201lb. The new population of pilots has normally distributed weights with a mean of158 lb and a standard deviation of 27.7 lb   If 32 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 201 lb.   The probability is approximately_________   . ​(Round to four decimal places as​ needed.)

the heights of 18-year old men are approximately normally distributed with a mean of U= 68 inches and a standard deviation of O=3. what is the probability that an 18-year-old mean selected at random is less than 65 inches tall.   a .8413 b .1587 c .1389 d .8765

Each month, an American household generates an average of 28 pounds of garbage.  Assume the standard deviation is 2.5 pounds.  If a household is selected at random, find the probability of the following:   A household averaging between 27 and 31 pounds per month   (5)             A household averaging more than 30.2 pounds per month      A street with 25 houses averaging more than 30 pounds per month.

Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other. What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more? 0.002 0.209 0.284 0.791

m&m's are packaged by weight, rather than by number of pieces, but consumers expect to have about 50 peices of candy in a single serving size bag. The number of pieces in a bag is normally distributed with a mean of 52.4 and a standard deviation of 2.2. a. Find the z-score corresponding to a bag with 47 pieces. Round your answer to 2 decimal places.     b. Find the probability of a bag containing 47 or fewer pieces. Round your answer to 4 decimal places.     c. A customer will be dissatisfied if they purchase a bag that contains fewer than 47 pieces. What percentage of customers will be dissatisfied? Round your answer to 2 decimal places.  %     The machine that packages the m&m's can be reset to change the average number per bag, although the variability (the standard deviation) will remain the same. What should the average be set to, in order to ensure that fewer than 1% of…

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1458 and the standard deviation was 312. The test scores of four students selected at random are 1860, 1220, 2150, and 1340. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1860 is (Round to two decimal plaes as needed.)

Need help with this problem

Use the following information to answer Questions #1 - 3. The amounts of time per workout that an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected athlete uses a stairclimber for between 24 and 31 minutes. Round to four decimal places as needed.