Question

The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.7, 5.0, 4.9, 5.5, 5.1, 5.7, 6.1. Is the process in control or out of control and why?It is out of control as one of these data points is more than 3 standard deviations from the meanIt is in control as one data point is more than 2 standard deviations from the meanIt is out of control as one data point is more than 2 standard deviations from the mean It is in control as the values jump above and below the mean

Answer 1

It is out of control as one data point is more than 2 standard deviations from the mean

Explanation:

Given that the soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams

We have mean - 3 sd =
`5.4-0.9 = 4.5`

Mean + 3sd =
`5.4+0.9 = 6.3`

The reading points are 5.8, 5.9, 4.9, 5.7, 5.0, 4.9, 5.5, 5.1, 5.7, 6.1.

On comparison we find that all points lie within 4.5 and 6.3

i.e. within 3 std deviations from the mean.

We get mean ±2 sigma as (4.8, 6)

We find 6.1 is outside this limit.

It is out of control as one data point is more than 2 standard deviations from the mean