A random sample of size n=400 is selected from a binomial distribution with popu

Question

A random sample of size n=400 is selected from a binomial distribution with population proportion p =.8
a) Find the probability that p (sample proportion) is greater than .83 b) Find the probability that p (sample proportion) lies between .76 and .84 A random sample of size n=400 is selected from a binomial distribution with population proportion p =.8
a) Find the probability that p (sample proportion) is greater than .83 b) Find the probability that p (sample proportion) lies between .76 and .84 A random sample of size n=400 is selected from a binomial distribution with population proportion p =.8
a) Find the probability that p (sample proportion) is greater than .83 b) Find the probability that p (sample proportion) lies between .76 and .84

Explanation / Answer

A random sample of size n=400 is selected from a binomial distribution with population proportion p =.8

a) Find the probability that p (sample proportion) is greater than .83

standard error =sqrt(0.8*.02/400) =0.02

z value for 0.83, z=(0.83-0.8)/0.02 =1.5

P( p> 0.83) =P( z >1.5)

= 0.0668

b) Find the probability that p (sample proportion) lies between .76 and .84

z value for 0.76, z=(0.76-0.8)/0.02 =-2.0

z value for 0.84, z=(0.84-0.8)/0.02 =2.0

P( 0.76<p<0.84) = P(-2.0<z<2.0)

= 0.9772 - 0.0228

=0.9544

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