MS 150 Statistics Spring 2000 Quickie Quiz Six

Statistic Equations Excel
Sample size n = COUNT(data)
Population size N
Sample mean xbar.gif (842 bytes) = sigmaxovern.gif (915 bytes) =AVERAGE(data)
=SUM(data)/COUNT(data)
Formulas for the population mean m = x P(x)
= n p
Sample Standard Deviation = sx
=sampstdev.gif (1072 bytes)		 =STDEV(data)
Population Standard Deviation = sigmax.gif (872 bytes)
=probabilitypopstdev.gif (1053 bytes)
= npq.gif (927 bytes)
Slope =SLOPE(y data, x data)
Intercept =INTERCEPT(y data, x data)
Correlation =CORREL(y data, x data)
Binomial probability = nCr pr q(n-r) =COMBIN(n,r)*p^r*q^(n-r)
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 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 xbar.gif (842 bytes) value given m and s xbartoz.gif (1022 bytes) =STANDARDIZE(x, m, s/SQRT(n))

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.)

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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