SOLUTION: The probalility that a tomato seed will germinate is 60%. A gardener plants in batches of 12. Round to the nearest 3 decimal places.
1. what is the probability that exactly 10 s
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Question 253060: The probalility that a tomato seed will germinate is 60%. A gardener plants in batches of 12. Round to the nearest 3 decimal places.
1. what is the probability that exactly 10 seeds will germinate?
2.what is the probability that all seeds will germinate?
3. what is the porbability that 10 or more seeds will germinate
4. Find the mean
5. Find the standard deviation
Answer by Greenfinch(383) (Show Source): You can put this solution on YOUR website!
This is a binomial distribution. B(12,0.6)
1.Exactly 10 seeds is 12C10 (0.6)^10 x (0.4)^2
this equates to 66 x 0.0060466 x 0.16 = 0.0638 or 6.38%
2. All seeds is 12C12 x (0.6)^12 x 1 = 0.00217678 or 0.22%
3. 10 or more are the 10, 11 and 12 cases added together. the case of 11 is
12C11 x (0.6)^11 x 0.4 = 12 x 0.0036797 x 0.4 = 0.017414 or 1.7414 %
So the probability of 10 or more is 6.38 + 1.74 + 0.22 % = 8.34%
4. The mean is the number of trials x probability or 12 x 0.6 = 7.2 successes
5. The variance is n x p x (1-p) which in this case is 12 x 0.6 x 0.4 = 2.88.
The standard deviation is the sqrt of this or 1.697.
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