MS 150 Statistics Spring 2001 Quiz Seven

DHL has found that the delivery time for packages is normally distributed with mean 14 hours and standard deviation 2 hours.

  1. For a package selected at random, what is the probability that it will be delivered in 18 hours or less?


  2. What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered on time?  (Hint: Note that 5% of the packages will be delivered beyond the guarantee time period.)
Statistic Equations Excel
Calculate a z value from an x z = standardize.gif (905 bytes) =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 -¥ to z. =NORMSDIST(z)
Calculate a z value from a probability where the probability is calculated from -¥ to z. =NORMSINV(probability)

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.

Standard normal distribution 0 to z: Table valuesStandard normal cumulative distribution left to z: Excel functions

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