Question

sample of 320 is drawn from a population with a proportion equal to 0.25. Determine the probability of observing between 74 and 93 successes. P(Observing between 74 and 93 ​successes)equals nothing

Answer 1

Solution

Given that,

p = 0.25

1 - p = 1 - 0.25 = 0.75

n = 320

= p = 0.25

  [p ( 1 - p ) / n] = [(0.25 * 0.75) / 320 ] = 0.0242

P( 0.23 < < 0.29 )

= P[(0.23 - 0.25) / 0.0242 < ( - ) / < (0.29 - 0.25) / 0.0242 ]

= P(-0.83 < z < 1.65)

= P(z < 1.65) - P(z < -0.83)

Using z table,   

= 0.9505 - 0.2033

= 0.7472