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

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?

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) )

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)

Sure, I can help you with that. Let's break down each part of the problem step by step.

A.) To find the probability that exactly 10 seeds will germinate, we can use the binomial probability formula. The formula is: P(x) = C(n, x) * p^x * (1 - p)^(n - x), where P(x) is the probability of getting exactly x successes, n is the total number of trials, p is the probability of success per trial, and C(n, x) represents the combination of choosing x successes out of n trials. In this case, n = 12 (since the gardener plants in batches of 12), p = 0.6 (60% chance of germination), and x = 10.

P(10) = C(12, 10) * 0.6^10 * (1 - 0.6)^(12 - 10)

To calculate C(12, 10), we can use the formula: C(12, 10) = 12! / (10! * (12-10)!)

Calculating all the above values will give you the probability that exactly 10 seeds will germinate.

B.) To find the probability that 10 or more seeds will germinate, we need to calculate the probabilities for 10, 11, and 12 seeds germinating, and then sum them up.

P(10 or more) = P(10) + P(11) + P(12)

To calculate P(11) and P(12), use the same binomial probability formula with x = 11 and x = 12, respectively.

C.) To find the probability that all seeds will germinate, we can use the binomial probability formula again, but this time with x = 12.

P(all) = P(12) = C(12, 12) * 0.6^12 * (1 - 0.6)^(12 - 12)

D.) To find the mean, we can use the formula for the expected value of a binomial distribution, which is given by the product of the number of trials and the probability of success per trial.

Mean = n * p

Substituting the values, you can find the mean.

E.) To find the standard deviation, we can use the formula for the standard deviation of a binomial distribution, which is the square root of the product of the number of trials, the probability of success per trial, and the probability of failure per trial.

Standard deviation = sqrt(n * p * (1 - p))

Substituting the values, you can find the standard deviation.

I hope this explanation helps you solve the problem!