I am having trouble figuring out how to do this type of problem. Here is the current problem I am working on:

Question

the probability that a tomato seed will germinate is 60%. A gardener plants in batches of 12.

A.) what is the probaility that exactly 10 seeds will germinate?

B.) what is the probability that 10 or more will germinate?

C.) what is the probability that all seeds will germinate?

D.) Find the mean.

E.) find the standard deviation.

Could someone please help me?

Answer 1

Your first 3 questions deal with binomial distribution in probability.

A) for exactly 10 out of 12
C(12,10) (.6)^10 (.4)^2
= 66(.00605)(.16)
= .0639

B) repeat the same calculations as above for
10 out of 12 + 11 out of 12 + 12 out of 12

C)that would be C(12,12)(.6)^12 = .002177
(you should have had the same result for the last part of B) )

Answer 2

I assume you refer to the batches of 12 planted seeds.

A)P(10) = (0.6)^10*(0.4)^2*[10!/(8!*2!)]
= 0.006047*0.16*(10*9/2)= 0.04359
B) Add P(10), P(11) and P(12)
P(11) = 0.6^11*0.4*10= 0.01451
See the next answer for P(12)

C) P(12) = (0.6)^12 = 0.00218
D) mean = (0.6)*12 = 7.2
E) sqrt[12*(0.6)(0.4)] = 1.70
(I'm not sure about the last one)