Mikes Resume shop specializes in creating resumes for studen

Mike\'s Resume shop specializes in creating resumes for students. A recent survey of Mike\'s shop revealed that a spelling error was made on 14% of the resumes last year. Assuming this rate continues into this month, and that they prepare 239 resumes this month, calculate the following probabilities

a) The probability that there are spelling errors on more than 32 resumes:

b) The probability that there are spelling errors on at least 32 resumes:

c) The probability that there are spelling errors on exactly 32 resumes:

Thank you!!!

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =239 * 0.14 = 33.46
Standard Deviation ( npq )= 239*0.14*0.86 = 5.3643
Normal Distribution = Z= X- u / sd                   
a)
P(X > 32) = (32-33.46)/5.3643
= -1.46/5.3643 = -0.2722
= P ( Z >-0.272) From Standard Normal Table
= 0.6064                  

b)
P(X < 32) = (32-33.46)/5.3643
= -1.46/5.3643= -0.2722
= P ( Z <-0.2722) From Standard NOrmal Table
= 0.3927                  
P(X>=32) = 1 - 0.6073

c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 31.5) = (31.5-33.46)/5.3643
= -1.96/5.3643 = -0.3654
= P ( Z <-0.3654) From Standard Normal Table
= 0.35741
P(X < 32.5) = (32.5-33.46)/5.3643
= -0.96/5.3643 = -0.179
= P ( Z <-0.179) From Standard Normal Table
= 0.42898
P(31.5 < X < 32.5) = 0.42898-0.35741 = 0.0716