This discussion introduces you to normal probability via the calculated zscore. A zscore converts a nonstandard normal distribution into a standard normal distribution; a standard normal distribution has a mean of zero and standard deviation of one.Additional zscore properties and details are provided later in the course. For this assignment, what is needed is the capability to calculate a zscore and find its associated probability (see Table A2 in your textbook). Here is an example:
Excel equation: z = (Your Score (X) – Mean)/(Standard Deviation) OR z = (X – Mean)/S.Zscore and probability calculation example:
Assume Intelligent Quotient (IQ) scores are normally distributed with a Mean of 100 and Standard Deviation of 15.Assume a friend has an IQ score of 130 (X).The zscore is then calculated: z = (130 – 100)/15 = 30/15 = 2.00.Find Table A2 in your textbook. The probability (green shaded area) associated with z = 2.00 is p = 0.9772.The probability of another friend scoring “higher” (nonshaded area) than 130 is: p = (1.0000 – 0.9772) = 0.0228 or 2.28%.
ScenarioDay 2 of the airshow arrives, and the weather is worsening. The temperature is 50oF, and strong thunderstorms are predicted. Continuing intermittent moderate to strong runway crosswinds (25 Knots sustained, with gusts to 40 Knots). Fortunately, all Day 2 flying sorties are accomplished with only minor incidents.Your team collected these simulated data for Day 2 flying sorties: attached below
In Microsoft Excel, complete the “Airshow – US Military Aircraft Performance” table by adding the calculated column and row values for mean, standard deviation, and zscore column values (use Sortie 10 data as the value of “X” in the zscore equation); report your calculated values to two decimal places (i.e., 0.12). For reporting probability, use Table A2 in your textbook and report the value of p to four decimal places (i.e., 0.1234).
Post the image of your spreadsheet into the discussion area along with a narrative of your findings before the fourth day of the module week to receive full credit.
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