Question

27. The daily high temperature for Chattanooga is normally distributed with mean 79 and standard deviation 4. Find the probability that a randomly chosen temperature is between 70 and 75.:* Oa. 0.0122 Ob. 0.1464 Oc. 0.1587 Od. 0.8413 28. At a certain school, 41% of the students play soccer, 30% play volleyball, and 14% play both soccer and volleyball. If a student is chosen at random, find the probability that he/she plays neither soccer nor volleyball.:* O a. 0.71 Ob. 0.57 Oc. 0.43 Od. 0.413

Answer 1

27. Let xbe the temperature randomly chosen. Given that x follows normal distrib- wion with mear M> 79 and standard deviation We need to calculate p (70<x< 75)=P(70-4 < x-H < 75-4) = P(7079 <2< 75-79) = P(-2.25<2<-1) z Area between -2-25 and -1 cended the standard noomal Area between -2-25 and o- Area between-lando Cenee مهمههههه 0-48778-0-34134 = 0.1464 Options 28 poobability that he/she plays either scacer or volleyball probability that student, play scocert poobability thed student play volleyball - poobability that the student play both soccer and voteyoodi Cas PČA0rb)=P(A)+pB)-plaand by 0-41 +0.30 -0.14 = 0.57 poo bability that he/she plays neettier Soccer noovo volleyball =1-0.51 - 0-43 ophanc

n = 29. Given that werght of a carton op strawberries has a mean Mo 1o and standard deviation Oz1.5. By central limit theorem ; for a sample size n greater than 30 ; Sample mean t will be apparimately normally distmbuted with mean of land standard error og Here - Sample size = 41 > 30 Hence we can apply the central limit theorem. Mean weight of the distribution of random sample with Size 0=41 will be oppoorimately noomal with mean Hz =4 = 16 and Standard errors 5x 1.5 0-234 6.40 Hence anscuer is mean-16, and standard errors appoo'ximately normal. Options 2 1.5 141 20.234;