Larsen Intro to Math Stat 5e The width of bolts of fabric i

Larsen - Intro to Math Stat 5e

The width of bolts of fabric is normally distributed with mean 950 mm (millimeters) and standard deviation 10 mm. What is the probability that a randomly chosen bolt has a width of between 947 and 958 mm?

Solution

Normal Distribution
Mean ( u ) =950
Standard Deviation ( sd )=10
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 947) = (947-950)/10
= -3/10 = -0.3
= P ( Z <-0.3) From Standard Normal Table
= 0.38209
P(X < 958) = (958-950)/10
= 8/10 = 0.8
= P ( Z <0.8) From Standard Normal Table
= 0.78814
P(947 < X < 958) = 0.78814-0.38209 = 0.4061