Question 1086671: A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability 0.70 of germinating. The biologist plants 10 seeds.
A.What is the probability that exactly 8 seeds will germinate? Round your answer to the nearest thousandths.
B.What is the probability that at least 8 seeds will germinate? Round your answer to the nearest thousandth.
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability 0.70 of germinating. The biologist plants 10 seeds.
A.What is the probability that exactly 8 seeds will germinate? Round your answer to the nearest thousandths.
B.What is the probability that at least 8 seeds will germinate? Round your answer to the nearest thousandth.
Solution:
To model a situation using the binomial distribution, the following criteria must be satisfied:
1. Bernoulli trials, i.e. exactly two possible outcomes (germinate or not)
2. Number of trials is known before and constant throught experiment,
i.e. independent of outcomes (n=10 seeds planted)
3. All trials are independent of each other (appropriate assumption for the current situation)
4. Probability of success is known, and remain constant throughout trials. (p=0.7, given)
Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given by
P(x)=C(N,x)(p^x)(1-p)^(N-x)
and,
C(N,x) is number of combinations of selecting x objects out of N.
(A) P(x=8)=C(10,8)p^x(1-p)^(n-x)
=45*0.7^8(1-0.7)^2
=45*.05764801*0.09
=0.233474
(B)
P(at least 8 seeds will germinate)
=P(8)+P(9)+P(10)
=0.233474+0.121061+0.028248
=0.38278
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