Question

10 Suppose that xres ppose thatx represents a random man's height. We want to know the probability that the man is between 72 etween 72 and 78 inches tall, usine probability notation, we represent this as P(72 SXS 78). Use the graph above to compute this probability P(72 sxs 78) = 0.135+ 0.0235 - 0,1585 11 Suppose again that represents a random man's height. Answer the following questions. about A P(x 2 75) = _0.0035 +0.001s = 0.029 B PIX 12) = 134+, 34+, 1357,0235= 0,84 between c P(63 < x < 78) = 135 + 4 + 3+ + 35+ , 0) 25 = 033 25 between DP(60 SX S66) = 0.0235 +0,35 = 0.1585 12 Remember, the Z-score of a value, x, is the number of standard deviations that x is from the mean, u. Put the Z-score below each x on the distribution of men's heights below. Z = X- M e z = 69-69 = 0 . 3. Z= 72-69 = 1 z=75-69 - 6=2 Z = 75-69 /0,34 / 0,34 10,34 0,34 35 0,0015 0.02 0.0015 002/0,158 / 02 Statway Version 3.1, 2018 WestEd. All rights reserved. 6.2.2 11

Answer 1

El (25 (13) Solution Here. Standard deviation Col= 3 since we said unusual if it is more than two standard deviations som the mean. se z> 20. ie. x > M+20 or x 09+2x3 x 75 Tor, x. fr. > 2x3 | 8 xy C9 - 6 (A) .. men with heights more than 75 inches fall are unusually fall men. Bla Comresponding Z-scores e X- -_ -75-09 - 2 = also, for unusually short mo, ronge of height will be below or less than two standard deviations from the mean. XZ 4-20 or X L 69-2X3 - 2 X L 63 o men with less than 63 incher fall are unusually short men. Ca Corresponding 2-gcons - Xo14 - 03-89 75-69 2 E -2