Question
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Answer:
0.2
Step-by-step explanation:
Given that:
P(particleboard with excessive bark) = 0.15
The P(that particleboard do not have excessive bark) = 1 - 0.15
i.e the population proportion number of success p = 0.85
The sample size (n) is given to be = 1000
To find the P(X ≥ 860)
Since the sample size is large, we will apply the normal approximation of binomial distribution to treat this question.
The population mean
The population standard deviation
Let X be the random variable which obeys a normal distribution;
Then;
P(X ≥ 860) = P(Z ≥ 0.8856)
P(X ≥ 860) = 1 - P(Z ≤ 0.8856)
From z table
P(X ≥ 860) = 1 - 0.8122
P(X ≥ 860) = 0.1878
P(X ≥ 860) 0.2
Thus, the probability of having more than 860 bark-free chips in a batch of 1,000 = 0.2