| Let X be normally distributed with mean = 16 and standard deviation = 12. Use Table 1. |
| a. | Find P(X 1).(Round \"z\" value to 2 decimal places and final answer to 4 decimal places.) |
| b. | Find P(X > 4). (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.) |
| c. | Find P(7 X 19). (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.) |
| d. | Find P(10 X 19).(Round \"z\" value to 2 decimal places and final answer to 4 decimal places.) |
| Let X be normally distributed with mean = 16 and standard deviation = 12. Use Table 1. |
Normal Distribution
Mean ( u ) =16
Standard Deviation ( sd )=12
Normal Distribution = Z= X- u / sd ~ N(0,1)
a)
P(X < 1) = (1-16)/12
= -15/12= -1.25
= P ( Z <-1.25) From Standard Normal Table
= 0.1056
b)
P(X > 4) = (4-16)/12
= -12/12 = -1
= P ( Z >-1) From Standard Normal Table
= 0.8413
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 7) = (7-16)/12
= -9/12 = -0.75
= P ( Z <-0.75) From Standard Normal Table
= 0.22663
P(X < 19) = (19-16)/12
= 3/12 = 0.25
= P ( Z <0.25) From Standard Normal Table
= 0.59871
P(7 < X < 19) = 0.59871-0.22663 = 0.3721
d)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 10) = (10-16)/12
= -6/12 = -0.5
= P ( Z <-0.5) From Standard Normal Table
= 0.30854
P(X < 19) = (19-16)/12
= 3/12 = 0.25
= P ( Z <0.25) From Standard Normal Table
= 0.59871
P(10 < X < 19) = 0.59871-0.30854 = 0.2902
Homework Sourse![Let X be normally distributed with mean = 16 and standard deviation = 12. Use Table 1. a. Find P(X 1).(Round \](/WebImages/15/let-x-be-normally-distributed-with-mean-16-and-standard-dev-1025764-1761531071-0.webp "Let X be normally distributed with mean = 16 and standard deviation = 12. Use Table 1. a. Find P(X 1).(Round \")
