Hours of TV A random sample of college students aged 18 to 24 years was obtained, and the number of hours of television watched in a typical week was recorded.

36.1 |
30.5 |
2.9 |
17.5 |
21.0 |

23.5 |
25.6 |
16.0 |
28.9 |
29.6 |

7.8 |
20.4 |
33.8 |
36.8 |
0.0 |

9.9 |
25.8 |
19.5 |
19.1 |
18.5 |

22.9 |
9.7 |
39.2 |
19.0 |
8.6 |

(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 weekly hours of television watched.

(d) Using the normal model from part (c), find the probability that a college student aged 18 to 24 years, selected at random, watches between 20 and 35 hours of television each week.

(e) Using the normal model from part (c), determine the proportion of college students aged 18 to 24 years who watch more than 40 hours of television per week.

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 - | (- |

36.1 | 15.196 | 230.9184 |

23.5 | 2.596 | 6.739216 |

7.8 | -13.104 | 171.7148 |

9.9 | -11.004 | 121.088 |

22.9 | 1.996 | 3.984016 |

30.5 | 9.596 | 92.08322 |

25.6 | 4.696 | 22.05242 |

20.4 | -0.504 | 0.254016 |

25.8 | 4.896 | 23.97082 |

9.7 | -11.204 | 125.5296 |

2.9 | -18.004 | 324.144 |

16 | -4.904 | 24.04922 |

33.8 |