Question

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate. Do not round your intermediate computations, and round your answer to three decimal places.

Answer 1

Complete question:

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 of them germinate.

Answer:

$P(x = 4) = 0.1376$

Step-by-step explanation:

Given

$n = 9$

$p = 63\%$ --- proportion that germinates

$p = 0.63$

Required

P(x = 4)

This question follows a binomial distribution:

$P(x) = ^nC_x*p^x*(1-p)^{n-x$

When x = 4;

$P(x = 4) = ^9C_4*0.63^4*(1-0.63)^{9-4$

$P(x = 4) = ^9C_4*0.63^4*(0.37)^5$

$P(x = 4) = 126*0.63^4*0.37^5$

$P(x = 4) = 0.13763895392$

$P(x = 4) = 0.1376$