## Answers

Let us first find the average across all samples = X-bar

Average of average of all samples = X-Dbar

We also need to find out the standard deviation of all the 30 samples

Let us calculate using excel as below -

Bag | ||||||

Sample | 1 | 2 | 3 | 4 | 5 | X-bar |

1 | 10.2 | 11.8 | 10.1 | 5.9 | 8.6 | 9.320 |

2 | 8.9 | 11.2 | 12.4 | 7.6 | 5.9 | 9.200 |

3 | 10.6 | 8.8 | 7.6 | 11.3 | 9.9 | 9.640 |

4 | 9.6 | 6.5 | 12.5 | 10.4 | 6.9 | 9.180 |

5 | 5.9 | 8.6 | 10.3 | 11.8 | 10.1 | 9.340 |

6 | 12.1 | 7.3 | 5.9 | 10.8 | 11.1 | 9.440 |

X-Dbar | 9.353 | |||||

stdev | 2.123 |

Hence, CL = X-Dbar = 9.353

Stdev = 2.123

Hence, UCL = CL + 3*stdev

=> UCL = 9.353 + 3*2.123 = 15.72

Hence, option (c) is the correct choice

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