The reading speed of sixthgrade students is approximately no

The reading speed of sixth-grade students is approximately normal with a mean speed of 125 words per minute and a standard deviation of 24 words per minutes. What is the probability that a randomly selected sixth-grade student reads less than 100 words per minutes?

Solution

Normal Distribution
Mean ( u ) =125
Standard Deviation ( sd )=24
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 100) = (100-125)/24
= -25/24= -1.0417
= P ( Z <-1.0417) From Standard Normal Table
= 0.1488                  
b)
P(X > 140) = (140-125)/24
= 15/24 = 0.625
= P ( Z >0.625) From Standard Normal Table
= 0.266                  
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 110) = (110-125)/24
= -15/24 = -0.625
= P ( Z <-0.625) From Standard Normal Table
= 0.26599
P(X < 130) = (130-125)/24
= 5/24 = 0.2083
= P ( Z <0.2083) From Standard Normal Table
= 0.58252
P(110 < X < 130) = 0.58252-0.26599 = 0.3165                  
d)
P(X > 200) = (200-125)/24
= 75/24 = 3.125
= P ( Z >3.125) From Standard Normal Table
= 0.0009                  
Yes it would unusual as it is below in 5% chance of occuring