tionid 1 falseicld MATH 1127 Intraduction oStaaicsCRN 11055

tionid 1 falseicld MATH 1127 Intraduction oStaaics-CRN 11055 Homework: Section 5.2 Homework Score: 0 of 10 pts 5.2.5 2of9(1 complete) Assume the random variable x is normally dstributed with mean -85 and standard devaten o-S Find the indicated probabm P(68 -x 80)- Round to four decimal places as needed.)

Solution

We are given that X ~ N(85,5²)

Required probability = P(68 < X < 80) = P[ (68-85) / 5 < Z < (80-85) / 5 ] = P( -3.4 < Z < -1 )

= P(Z<-1) - P(Z<-3.4) = P(Z>1) - P(Z>3.4) = [1 - P(Z<1)] - [1- P(Z<3.4)] = P(Z<3.4) - P(Z<1) = 0.99966 - 0.84134 = 0.15832 ~ 0.1583