How to solve this problem (2+3i)2
2 answers:
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Answer:
a) 0.4352
b) 0.5165
c) 0.0813
Step-by-step explanation:
In this problem we have 3 defective parts scattered among 15 parts.
We are going to select 3 out of 15 without replacement, so the situation can be modeled with the Hypergeometric distribution.
If X is the random variable that measures the number of defective parts in a sample of 3, the probability of selecting exactly k defective parts out of 15 would be given by
a) what is the probability that the inspector finds exactly one nonconforming part?
Replacing k with 1 in our previous formula, we get
b) what is the probability that the inspector finds at least one nonconforming part?
This would be P(X=1)+P(X=2)+P(X=3) = 1 - P(X=0).
so 1 - P(X=0) = 1 - 0.4835 = 0.5165
c) what is the probability that the inspector finds at least two nonconforming part?
P(X=2) + P(X=3) = 1 - (P(X=0) + P(X=1)) = 1 - (0.4835 + 0.4352) =
= 1 - 0.9187 = 0.0813
Step-by-step explanation:
a) The graph of a normal curve with a mean of 64" and a standard deviation of 3.5" is a bell-shaped curve with its
maximum value at x = 64.
Important points:
mean - 3 deviations: 64 - 3(3.5) = 64 - 10.5 = 53.5
mean - 2 deviations: 64 - 2(3.5) = 64 - 7 = 57
mean - 1 deviation: 64 - 3.5 = 60.5
mean: = 64
mean + 1 deviation: 64 + 3.5 = 67.5
mean + 2 deviations: 64 + 2(3.5) = 64 + 7 = 71
mean + 3 deviations: 64 + 3(3.5) = 64 + 10.5 = 74.5
b) If there are 3000 plants, approximately how many will be taller than 71"?
71" is 2 standard deviations above the mean. The region between two standard deviations below the mean and two standard deviations holds approximately 95% of the plants.
Therefore there will be approximately 5% of the plants divided equally between being taller than two standard
deviations above the mean and being shorter than two standard deviations below the mean. Thus, there will be
approximately 2.5% of the plants taller than 71": 0.025 x 3000 = 75 plants.
or
the z-score for 71
= (71-64)/35 = 2
going to your tables, or some other suitable source for standard deviation, we find
P(z < 2) = .9772
P(z > 2) = .0228
.0228(3000) = 68.4
or appr 68 plants
