Suppose 70 of high school students carry a cell phone In a s

Suppose 70% of high school students carry a cell phone. In a sample of 175 high school students, what is the probability that between 20% and 30% of them do not carry a cell phone?

Solution

Normal Distribution
Proportion ( P ) =0.3
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.3*0.7/175)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.2) = (0.2-0.3)/0.0346
= -0.1/0.0346 = -2.8902
= P ( Z <-2.8902) From Standard Normal Table
= 0.00193
P(X < 0.3) = (0.3-0.3)/0.0346
= 0/0.0346 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(0.2 < X < 0.3) = 0.5-0.00193 = 0.4981