The mean and standard deviation of the random variable Round

The mean and standard deviation of the random variable. (Round your \"\" to 4 decimal places and mean to 1 decimal place.)

The probability that X is 18 or more. (Use the rounded values found above. Round your answer to 4 decimal places.)

The probability that X is 12 or less. (Use the rounded values found above. Round your answer to 4 decimal places.)

Solution

Normal Distribution
a)
Mean ( np ) =15.6
Standard Deviation ( npq )= 60*0.26*0.74 = 3.3976
Normal Distribution = Z= X- u / sd   
              
b)
P(X < 18) = (18-15.6)/3.3976
= 2.4/3.3976= 0.7064
= P ( Z <0.7064) From Standard Normal Table
= 0.76                  
P(X > = 18) = (1 - P(X < 18)
= 1 - 0.76 = 0.24                  

c)
P(X > 12) = (12-15.6)/3.3976
= -3.6/3.3976 = -1.0596
= P ( Z >-1.06) From Standard Normal Table
= 0.8553                  
P(X < = 12) = (1 - P(X > 12)
= 1 - 0.8553 = 0.1447