Constructing Normal Quantile Plots. In Exercises 17−20, use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution.

Braking Distances A sample of braking distances (in feet) measured under standard conditions for a sample of large cars from Data Set 14 in Appendix B: 139, 134, 145, 143, 131.

Answer :

Step 1 of 1 :

Given Braking Distances A sample of braking distances (in feet) measured under standard conditions for a sample of large cars from Data Set 14:

139, 134, 145, 143, 131.

First sort the data by arranging the values in order from lowest to highest.

131,134,139,143,145

x-values |

131 |

134 |

139 |

143 |

145 |

Here n = 5

Then we have to identify the cumulative areas to the left of the corresponding values.

Here from the above table we have P(z) and z-score can be calculated by using standard normal table(area under normal curve)

P(z) |
z -score |

0.1 |
-1.28 |

0.3 |
-0.52 |

0.5 |
0 |

0.7 |
0.52 |

0.9 |
1.28 |

Now we have to plot a normal quantile plot.

x-values |
z -score |

131 |
-1.28 |

134 |
-0.52 |

139 |
0 |

143 |
0.52 |

145 |
1.28 |

We are using excel to draw a normal quantile plot.

So we have to follow steps

Then the steps are given below

1.Enter x values in one column and z-scores in other column

2.Select two columns then go to insert

3.Select scatterplot

4.Choose layout in that sect quantile plot

4.Then press ok

We get the normal quantile plot.

If the normal quantile plot is roughly linear(roughly a straight line), then the sample data is approximately normal distributed.From the above graph we can say that the given data is not normal because plotted points are not near to trend line hence it is not normal.