Question

Suppose that I buy a packet of seeds that carries the claim that the germination rate for seeds of this type is 93%. Assume that my packet of seeds contains a random sample of seeds, so that the germination of one seed is independent of the germination of any other seed. If there are 120 seeds in this packet, what is the approximate probability that I get a germination rate of less than 0.9? That is, what is P(p-hat < 0.9)?

0.099

0.725

0.901

0.512

0.488

Answer 1

Given that,

p = 0.93

1 - p = 0.07

n = 120

= p = 0.93

=  [p ( 1 - p ) / n] =   [(0.39 * 0.07) / 120 ] = 0.0233

P( < 0.9) =

= P[( - ) / < (0.9 - 0.93) / 0.0233]

= P(z < -1.287)

= 0.099