Question

Question 13 4 pts Z-scores A variable is normally distributed, with mean 118 and standard deviation 30. What is the Z-score when x = 100? (Select] What x value is 1.5 standard deviations above the mean? [Select) > Question 14 6 pts Normal Distribution A variable is normally distributed, with mean 118 and standard deviation 30. What is P(60 SXS 160)? (Select) What is P(x2130)? Select) What is the top 10%? [Select

Answer 1

Question (13) Given, l= 118 os 30 i) when x= 100 then Z-score is, X-4 100 T8 30 I-score - 0.6 |z-scorel = 0.6. Z=1.5, the I-score is, - Scores x- el find, x, x = 4+ J. 2 score 118 4 30* 1.5 X = 163 Question (4) let x O NIM, 92), M=118, 30. 60-4 i P (60 2 x 160) = P (60 szę 160-4) - P (60 60 -118 30 CIL 160-118 30 - PC -1,933 <z? 1.4) = $(1.4) – $(-1.9333)

using std Normal rable we gel - P(6osas 160) 0.9192 -0.02659 0.8926 P ( 605 xs 160) = 0.8926 P ( x 7, 130) 1 - PCXS130) = 1- P(2¢130-4) a = 1- P(Z 130-118 = P(Z < 0.4) I-d(0.4) = - 0.6554 :| PC P ( X 7, 130) = 0.34457 10x 0.8926 8.926% The top 10% is,