Chips per BagĀ In a 1998 advertising campaign, Nabisco claimed that every 18-ounce bag of Chips Ahoy! Cookies contained at least 1000 chocolate chips. Brad Warner and Jim Rutledge tried to verify the claim. The following data represent the number of chips in an 18-ounce bag of Chips Ahoy! based on their study.

1087 |
1098 |
1103 |
1121 |
1132 |

1185 |
1191 |
1199 |
1200 |
1213 |

1239 |
1244 |
1247 |
1258 |
1269 |

1307 |
1325 |
1345 |
1356 |
1363 |

1135 |
1137 |
1143 |
1154 |
1166 |

1214 |
1215 |
1219 |
1219 |
1228 |

1270 |
1279 |
1293 |
1294 |
1295 |

1377 |
1402 |
1419 |
1440 |
1514 |

Source: ChanceĀ 12(1): 10-14, 1999 |

(a) Use the following normal probability plot to determine if the data could have come from a normal distribution.

(b) Determine the mean and standard deviation of the sample data.

(c) Using the sample mean and sample standard deviation obtained in part (b) as estimates for the population mean and population standard deviation, respectively, draw a graph of a normal model for the distribution of chips in a bag of Chips Ahoy!.

(d) Using the normal model from part (c), find the probability that an 18-ounce bag of Chips Ahoy! selected at random contains at least 1000 chips.

(e) Using the normal model from part (c), determine the proportion of 18-ounce bags of Chips Ahoy! that contains between 1200 and 1400 chips, inclusive.

Answer :

Step 1 :

a)

From the plot, we see that the points on the pattern lie close to the straight line and it indicates that the sample data could have come from a population that is normally distributed.

b)

...x | x - | (- | ||

1087 | -160.4 | 25728.16 | ||

1185 | -62.4 | 3893.76 | ||

1239 | -8.4 | 70.56 |