A company claims that the number of defective items manufactured during each run of making 100 of their products is independent of the number from other runs and that the proportion of defectives is not more than 4%, Assuming that the proportion of defectives of each runis 4%, which statement (s) is (are) true to determine whether x=10 is unusually a high number of defective items on the next run of 100 products?

The statements that are true to determine whether x=10 is unusually high number of defective items on the next run of 100 products are given by the following option:

I and III.

What are unusually high measures in the binomial distribution?

Unusual values in the normal distribution are found using the range rule of thumb, which states that if a value is more than two standard deviations from the mean, the measure is unusual.

The measures for the binomial distribution are given as follows:

E(X) = np.

S(X) = sqrt(np(1 - p)).

The parameters for this problem are given as follows:

n = 100, p = 0.04.

Then the mean and the standard deviation are given as follows:

Mean: 4.

Standard deviation: 1.96.

Thus the upper bound for usual values is of:

4 + 2 x 1.96 = 7.92.

Which is less than 10, hence 10 is an unusual measure and statement I is correct.

Statement III is also correct, as:

P(X >= 10) < 0.05.

While statement II is false, as we do not look at the exact measure, but an interval of measures.

Missing Information

The problem is given by the image shown at the end of the answer.

More can be learned about the binomial distribution at https://brainly.com/question/24756209

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