According to the school board 48 of all the voters in the di

According to the school board, 48% of all the voters in the district support the referendum. Suppose that a principal is interested in the proportion of voters who support the referendum in a group of 38 parents. Let r be a random variable that represents the voters in the district that support the referendum. The school board wants a probability distribution for r.

a. Find the mean and standard deviation

b. Estimate P(r 25)

P(r 25) = P( ) = P( ) = _______________

c. Estimate P(15 r 25)

P(15 r 25) = P( ) = P( ) = ____________

Solution

Normal Approximation to Binomial Distribution
a)
Mean ( np ) =38 * 0.48 = 18.24
Standard Deviation ( npq )= 38*0.48*0.52 = 3.0797
Normal Distribution = Z= X- u / sd                   
b)
P(X >= 25) = (25-18.24)/3.0797
= 6.76/3.0797 = 2.195
= P ( Z >2.195) From Standard Normal Table
= 0.0141                  
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X <= 15) = (15-18.24)/3.0797
= -3.24/3.0797 = -1.0521
= P ( Z <-1.0521) From Standard Normal Table
= 0.14639
P(X <= 25) = (25-18.24)/3.0797
= 6.76/3.0797 = 2.195
= P ( Z <2.195) From Standard Normal Table
= 0.98592
P(15 <= X <= 25) = 0.98592-0.14639 = 0.8395