Question 2 Fill-In-The-Blank Worth 3 points)
1 answer:
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Answer:
a)
b)
Step-by-step explanation:
The proportion of defective gadgets for this factory is p=0.2.
If a sample of n=100 gadgets is taken from the production, we can model the amount of defectives gadgets in this sample as a binomial random variable.
The probability of having k defectives in the sample can be written as:
Then, we can write the expression to calculate the probabilities of A: "less than 15 gadgets are mildly defective":
If we approximate this binomial distribtution to a normal distribution, we can calculate the new parameters as:
The continuity factor is applied for the change from a discrete distribution (binomial) to a continous distribution (normal). Then we have:
Now, we can calculate the probability P(A):