Question

Given a population where the probability of success is p=0.35 calculate the probabilities below if a sample of 600 is taken.

a.	Calculate the probability the proportion of successes in the sample will be less than 0.36?
b.	What is the probability the proportion of successes in the sample will be greater than 0.38?

​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that ,

p = 0.35

1 - p = 0.65

n = 600

= p = 0.35

= (p*(1-p))/n =  (0.35*0.65)/600 = 0.01947

a)

P( <0.36 ) = P(( - ) / < (0.36 - 0.35) / 0.01947)

= P(z < -0.513)

= 0.6960

Probability = 0.6960

b)

P( > 0.38) = 1 - P( < 0.38)

= 1 - P(( - ) / < (0.38-0.35) /0.01947 )

= 1 - P(z < 1.54)

= 1 - 0.9382

= 0.0618

Probability = 0.0618