Question

The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. The company takes readings of every 10th bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why? Use a control chart to answer the question.
It is out of control as the values jump above and below the mean

It is out of control as one of these data points is more than 3 standard deviations from the mean

It is out of control as two of these data points are more than 2 standard deviations from the mean

It is out of control as at least two of three consecutive data points are more than 2 standard deviations from the mean

Answer 1

The correction option is B, It is out of control as one of these data points is more than 3 standard deviations from the mean.

What is Normal Distribution?

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. Therefore, the maximum and the minimum weight of the candy can be,

Maximum weight = Mean + 3(Standard deviation)

                             = μ + 3σ

                             = 16.1 + 3(0.9)

                             = 16.1 + 2.7

                             = 18.8

Minimum weight = Mean - 3(Standard deviation)

                            = μ - 3σ

                            = 16.1 - 3(0.9)

                            = 16.1 - 2.7

                            = 13.4

Since one of the reading point, 19.4 is more than 3 standard deviations from the mean, therefore, it can be concluded that the process is out of control.

Hence, It is out of control as one of these data points is more than 3 standard deviations from the mean.

Learn more about Normal Distribution here:

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