On the following four graphs the distribution of the x data is shown by the black outline histogram columns. The x distribution is the same for all four graphs. The distribution of 40 sample means () is shown by the grey solid histogram columns. The first two questions that follow the graphs pertain to these four graphs.

- What is the shape of the x distribution?

- Circle the graph which most likely best depicts the distribution of the sample means ( distribution).

Statistic | Equations | Excel |
---|---|---|

Calculate a z value from an x | ^{z = } |
=STANDARDIZE(x, m, s) |

Calculate an x value from a z | x = s z + m | |

Calculate a cumulative probability from a z value where the probability is
calculated from negative infinity to z. |
=NORMSDIST(z) | |

Calculate a z value from a probability where the probability is calculated from
negative infinity to z. |
=NORMSINV(probability) | |

Calculate a z value from an value given m and s | =STANDARDIZE(x, m, s/SQRT(n)) |

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed with mean m = 35 minutes and standard deviation s = 7 minutes.

- What is the probability that a first interview will last 40 minutes or longer?

- Nine first interviews are usually scheduled per day. What is the probability that
the average length of time for the nine interviews will be 40 minutes or longer?

Table of standard normal probabilities from 0 to z. For values of z larger than 2.69 use 0.497.

0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | |
---|---|---|---|---|---|---|---|---|---|---|

0.0 | 0.000 | 0.004 | 0.008 | 0.012 | 0.016 | 0.020 | 0.024 | 0.028 | 0.032 | 0.036 |

0.1 | 0.040 | 0.044 | 0.048 | 0.052 | 0.056 | 0.060 | 0.064 | 0.067 | 0.071 | 0.075 |

0.2 | 0.079 | 0.083 | 0.087 | 0.091 | 0.095 | 0.099 | 0.103 | 0.106 | 0.110 | 0.114 |

0.3 | 0.118 | 0.122 | 0.126 | 0.129 | 0.133 | 0.137 | 0.141 | 0.144 | 0.148 | 0.152 |

0.4 | 0.155 | 0.159 | 0.163 | 0.166 | 0.170 | 0.174 | 0.177 | 0.181 | 0.184 | 0.188 |

0.5 | 0.191 | 0.195 | 0.198 | 0.202 | 0.205 | 0.209 | 0.212 | 0.216 | 0.219 | 0.222 |

0.6 | 0.226 | 0.229 | 0.232 | 0.236 | 0.239 | 0.242 | 0.245 | 0.249 | 0.252 | 0.255 |

0.7 | 0.258 | 0.261 | 0.264 | 0.267 | 0.270 | 0.273 | 0.276 | 0.279 | 0.282 | 0.285 |

0.8 | 0.288 | 0.291 | 0.294 | 0.297 | 0.300 | 0.302 | 0.305 | 0.308 | 0.311 | 0.313 |

0.9 | 0.316 | 0.319 | 0.321 | 0.324 | 0.326 | 0.329 | 0.331 | 0.334 | 0.336 | 0.339 |

1.0 | 0.341 | 0.344 | 0.346 | 0.348 | 0.351 | 0.353 | 0.355 | 0.358 | 0.360 | 0.362 |

1.1 | 0.364 | 0.367 | 0.369 | 0.371 | 0.373 | 0.375 | 0.377 | 0.379 | 0.381 | 0.383 |

1.2 | 0.385 | 0.387 | 0.389 | 0.391 | 0.393 | 0.394 | 0.396 | 0.398 | 0.400 | 0.401 |

1.3 | 0.403 | 0.405 | 0.407 | 0.408 | 0.410 | 0.411 | 0.413 | 0.415 | 0.416 | 0.418 |

1.4 | 0.419 | 0.421 | 0.422 | 0.424 | 0.425 | 0.426 | 0.428 | 0.429 | 0.431 | 0.432 |

1.5 | 0.433 | 0.434 | 0.436 | 0.437 | 0.438 | 0.439 | 0.441 | 0.442 | 0.443 | 0.444 |

1.6 | 0.445 | 0.446 | 0.447 | 0.448 | 0.449 | 0.451 | 0.452 | 0.453 | 0.454 | 0.454 |

1.7 | 0.455 | 0.456 | 0.457 | 0.458 | 0.459 | 0.460 | 0.461 | 0.462 | 0.462 | 0.463 |

1.8 | 0.464 | 0.465 | 0.466 | 0.466 | 0.467 | 0.468 | 0.469 | 0.469 | 0.470 | 0.471 |

1.9 | 0.471 | 0.472 | 0.473 | 0.473 | 0.474 | 0.474 | 0.475 | 0.476 | 0.476 | 0.477 |

2.0 | 0.477 | 0.478 | 0.478 | 0.479 | 0.479 | 0.480 | 0.480 | 0.481 | 0.481 | 0.482 |

2.1 | 0.482 | 0.483 | 0.483 | 0.483 | 0.484 | 0.484 | 0.485 | 0.485 | 0.485 | 0.486 |

2.2 | 0.486 | 0.486 | 0.487 | 0.487 | 0.487 | 0.488 | 0.488 | 0.488 | 0.489 | 0.489 |

2.3 | 0.489 | 0.490 | 0.490 | 0.490 | 0.490 | 0.491 | 0.491 | 0.491 | 0.491 | 0.492 |

2.4 | 0.492 | 0.492 | 0.492 | 0.492 | 0.493 | 0.493 | 0.493 | 0.493 | 0.493 | 0.494 |

2.5 | 0.494 | 0.494 | 0.494 | 0.494 | 0.494 | 0.495 | 0.495 | 0.495 | 0.495 | 0.495 |

2.6 | 0.495 | 0.495 | 0.496 | 0.496 | 0.496 | 0.496 | 0.496 | 0.496 | 0.496 | 0.496 |

The above table shows the standard normal probability from 0 to z as seen at the left below. The Excel functions use left to z as shown at the right below.