Question

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,500,000 and whose population proportion with a specified characteristic is p = 0.56. Complete parts (a) through (C) below. (b) What is the probability of obtaining x = 590 or more individuals with the characteristic? P(x2 590) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 540 or fewer individuals with the characteristic? P(x5540) = (Round to four decimal places as needed.)

Answer 1

Answer:-

Given that:-

n=1000 , N=1,500,000 and p=0.56

mean of sampling distribution p=0.56

sd$=\sqrt{\frac{P*(1-P)}{n}}$

$=\sqrt{\frac{0.56*(1-0.56)}{1000}}$

$=0.0156971335$

b)P(P>590/1000)

=1-P(P>0.59)

=1-P(z>(0.59-0.56)/0.0156971335)

=1-P(Z>1.914323)

=1-0.0281

=0.9719

c)

P(P<540/1000)

=1-P(P<0.54)

=1-P(z<(0.54-0.56)/0.0156971335)

=1-P(Z<-1.274117)

=1-0.8980

=0.1020