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 10^th 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?

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 in control as the data points more than 2 standard deviations from the mean are far apart

It is in control as the values jump above and below the mean

Answer 1

Answer :

Given data :-

The candy produced by a company has a sugar level that is normally distributed

with a mean is  = 16.1

  $\mu$ = 16.1

standard deviation = 0.9

  $\sigma$ = 0.9

  $\mu$ +/- 2 $\sigma$ ( within 2 SD's from mean )

=> 16.1 +/- 2(0.9)

=> 16.1 +/- 1.8

=> 16.1-1.8

=> 14.2

=> 16.1+1.8

=> 17.9

The data points 14.9 and 19.4 are out of 2.SD's

from mean

$\therefore$ the correct answer is

option : 2

that is

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