Question

15. [-16 Points] DETAILS AUFEXC4 13.4.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the table to answer the question. Note: Round 2-scores to the nearest hundredth and then find the required A values using the table. A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 54.9 mm and a standard deviation of 2.9 mm. What percent of the butterflies had the following wingspans? (Round your answers to one decimal place.) (a) less than 48.6 mm % (b) between 49 and 55 mm % Need Help? Read It Talk to a Tutor 16. [-/10 Points] DETAILS AUFEXC4 13.4.040. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the table to answer each question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table. A psychologist finds that the intelligence quotients of a group of patients are normally distributed, with a mean of 102 and a standard deviation of 16. Find the percent of the patients with the following IQS? (a) above 114 % (b) between 90 and 120 Need Help? Read It Talk to a Tutor

Answer 1

Ans/15 let X is random Variable and distribution then it is denoted as - follows Nenmal XNN (4,22) el = Mean o2= Variance o=Jož= Standard deviation. In our Case x~ N(54-2,12-9) z = x- M=54.9 CScanned with CamScanner and 5 =2-9 mm

a P (x <48.6) < 118 6 -syg 2.9 G P(x-4 = P(z <-2.1724137) = P(Z <-2017) [P(x. 48.6) = 0.015 0 p(x<usc) = 11-50 % = 10 1.5 (After round off to one deima = <z< 55-54.9 2.9 © P (649<x<55) P(u ug-su-g 2.9 P(-2.0344 <2<0-03448) P(220.03 uus) - P(Z < -2.0344) = P(Z <0.03) - P(Z <-2-63) = 0.5120 P(ug<x<ss) O-4908 plus <x<ss) = 49.08 % 49.1 % after some of to one decimal 0.0212 Scanned with CamScanner

And 16: IXNN (102, 16 @ f (x > 114) P(z) 11-102 Plz > 0.75) 1-P (Z50-75) =1 0.7734 1 P(x >l14) = 0.2266 CScanned with Cameloverliy 22.66 0/0

P 16. 16 P(90<x< 120) = go-102 < ZL 120-102 = P(-0-75 < 2 < 1-25) = P(Z < 1.125 1 - P(Z<-075) = p (2<1-13) – PLZ2-0.75) = 0.8708 – 0-2266 P(90<x< 120) = 0-6442 between 90 &120 164.42% Owe (17 a- b Strongest positive linear correlation blw xey variables > Graph b b Strongest negative the X ey Variables lineam Correlation b/w the x С. Graph © Scanned with CamScanner