The number of defects in a random sample of 200 parts produced by a machine is binomially distributed with p = .03. Based on this information, the expected number of defects in the sample is 6.
Is it True or False?
in a scientfic study there are 8 pigs 5 of which are pregnant if three are selected at random without replacement find the probability that all are pregant
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False. The expected number of defects in the sample can be calculated by multiplying the probability of a defect (p = 0.03) by the number of trials (n = 200). Therefore, the expected number of defects in the sample is 0.03 * 200 = 6.
Thus, the statement "The expected number of defects in the sample is 6" is true.
True.
To determine whether the statement is true or false, we need to calculate the expected number of defects in the sample.
In a binomial distribution, the expected value (also known as the mean) is calculated as the product of the number of trials (sample size) and the probability of success.
Given that the sample size is 200 parts and the probability of a defect is 0.03, we can calculate the expected number of defects in the sample using the following formula:
Expected number of defects = Sample size * Probability of a defect
Expected number of defects = 200 * 0.03
Expected number of defects = 6
Therefore, the statement is true. The expected number of defects in the sample is 6.