5. One piece of PVC pipe is to be inserted inside another piece. The overlap should be normally distributed with mean 1 inch and sd 0.1. The lengths of the pieces are independent and normally distributed: for piece 1 the mean is 20 and sd 0.5 inches; for piece 2 the mean is 15 and sd 0.4 inches. Find the probability that the total length after insertion is between 34.5 and 35 inches.

step-by-step explanation:

; fx

my guess would be b and d, but i didn’t actually get out the pen and paper. lol

none of these

step-by-step explanation:

23 + 34 add up to 57 so just inform the teacher of this really stupid mistake

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.