<p>In a vegetable farm, a sample of $35$ produce is randomly selected from a production batch. The batch will be rejected if there are more than $3$ rotten produce and will be accepted if it has less than $3$. If the number of rotten produce is exactly $3$, another sample of $25$ produce will be randomly selected form the production batch, the batch is rejected if the $2^{\mathrm{nd}}$ sample has more than $1$ rotten produce, otherwise the batch is accepted. Given that the proportion of defective produce is $8%$ of the total produce at the farm.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the probability that the batch is accepted as a result of the $1^{\mathrm{st}}$ sample.</div></li><li><div class="list-item-paragraph">Given that a $2^{\mathrm{nd}}$ sample is selected from inspection, find the probability that the batch will be rejected.</div></li><li><div class="list-item-paragraph">Find the probability that the batch will be rejected..</div></li><li><div class="list-item-paragraph">It is given that $0.15$ hours are required for the inspection of each product thoroughly. Find the expected number of hours required for the inspection of a batch at the plant.</div></li></ol>

In a vegetable farm, a sample of $35$ produce is randomly selected from a production batch. The batch will be rejected if there are more than $3$ rotten produce and will be accepted if it has less than $3$. If the number of rotten produce is exactly $3$, another sample of $25$ produce will be randomly selected form the production batch, the batch is rejected if the $2^{\mathrm{nd}}$ sample has more than $1$ rotten produce, otherwise the batch is accepted. Given that the proportion of defective produce is $8%$ of the total produce at the farm.

Find the probability that the batch is accepted as a result of the $1^{\mathrm{st}}$ sample.

Given that a $2^{\mathrm{nd}}$ sample is selected from inspection, find the probability that the batch will be rejected.

Find the probability that the batch will be rejected..

It is given that $0.15$ hours are required for the inspection of each product thoroughly. Find the expected number of hours required for the inspection of a batch at the plant.

Binomial Distribution

Question 18c37cc9

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