Blood type AB is found in only 3 of the population If 345 pe

Blood type AB is found in only 3% of the population†. If 345 people are chosen at random, find the probability of the following. (Use the normal approximation. Round your answers to four decimal places.)

(a) 5 or more will have this blood type

(b) between 5 and 10 will have this blood type

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =345 * 0.03 = 10.35
Standard Deviation ( npq )= 345*0.03*0.97 = 3.1685
Normal Distribution = Z= X- u / sd   
a)              
P(X < 5) = (5-10.35)/3.1685
= -5.35/3.1685= -1.6885
= P ( Z <-1.6885) From Standard NOrmal Table
= 0.0457                  
P( X >= 5) = 1 - P(X < 5) = 0.9543  

b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 5) = (5-10.35)/3.1685
= -5.35/3.1685 = -1.6885
= P ( Z <-1.6885) From Standard Normal Table
= 0.04566
P(X < 10) = (10-10.35)/3.1685
= -0.35/3.1685 = -0.1105
= P ( Z <-0.1105) From Standard Normal Table
= 0.45602
P(5 < X < 10) = 0.45602-0.04566 = 0.4104