Select one a 0 b 1 c 106 d 106SolutionMean u 110 Standard

Select one:

a. 0

b. 1

c. 1.06

d. -1.06

Solution

Mean ( u ) =110
Standard Deviation ( sd )=5.65
Number ( n ) = 12
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 103.5) = (103.5-110)/5.65/ Sqrt ( 12 )
= -6.5/1.631
= -3.9852
= P ( Z <-3.9852) From Standard Normal Table
= 0.00003
P(X < 104.5) = (104.5-110)/5.65/ Sqrt ( 12 )
= -5.5/1.631 = -3.3721
= P ( Z <-3.3721) From Standard Normal Table
= 0.00037
P(103.5 < X < 104.5) = 0.00037-0.00003 = 0.0003   ~ 0