a seed company advertises that, if its seeds are properly planted, 95% of them will germinate. What is the probability that, when 20 seeds are properly planted, at least 15 will germinate -
pM( 19/20)? pq(1/20)?
20c15
20c16 all the way up to 20C10?
Don't know if I am setting this up correctly
To find the probability that at least 15 seeds will germinate out of 20, you can use the binomial probability formula. The formula is:
P(x) = C(n, x) * p^x * q^(n-x)
Where:
P(x) is the probability of getting exactly x successes.
C(n, x) is the number of combinations of n items taken x at a time.
p is the probability of success on a single trial.
q is the probability of failure on a single trial.
n is the total number of trials.
In this case, let's set up the calculation step by step:
Step 1: Determine the individual probabilities:
p = 0.95 (95% germination rate)
q = 0.05 (5% failure rate)
Step 2: Calculate the probability of getting exactly x successes:
P(x = 15) = C(20, 15) * p^15 * q^(20-15)
P(x = 16) = C(20, 16) * p^16 * q^(20-16)
P(x = 17) = C(20, 17) * p^17 * q^(20-17)
P(x = 18) = C(20, 18) * p^18 * q^(20-18)
P(x = 19) = C(20, 19) * p^19 * q^(20-19)
P(x = 20) = C(20, 20) * p^20 * q^(20-20)
Step 3: Sum up the probabilities of all possible outcomes:
P(at least 15 germinate) = P(x = 15) + P(x = 16) + P(x = 17) + P(x = 18) + P(x = 19) + P(x = 20)
Using this setup, you can calculate the individual probabilities and then sum them up to find the probability that at least 15 seeds will germinate.
Note: In your question, you mentioned "pM(19/20)" and "pq(1/20)," which are not clear. It seems you may have made some calculation errors. Please refer to the step-by-step process provided above to set up the correct calculations.