Costumers take fre samples in about 60 of the cases When 317

Costumers take fre samples in about 60% of the cases. When 317 costumers are observed, what is the probability that more than 180 will take a sample?

Please show me your calculations

Solution

mean= n*p=317*0.6 =190.2

standard deviation= sqrt(n*p*(1-p)) =sqrt(317*0.6*0.4) =8.722385

So the probability that more than 180 will take a sample is

P(X>180) =P((X-mean)/s >(180-190.2)/8.722385)

=P(Z>-1.17) =0.8790 (from standard normal table)