Question

This discussion introduces you to normal probability via the calculated z-score. A z-score converts a non-standard normal distribution into a standard normal distribution; a standard normal distribution has a mean of zero and standard deviation of one.
This discussion introduces you to normal probability via the calculated z-score. A z-score converts a non- standard normal distribution into a standard normal distribution; a standard normal distribution has a mean of zero and standard deviation of one. Additional z-score properties and details are provided later in the course. For this assignment, what is needed is the capability to calculate a z-score and find its associated probability (see Table A-2 in your textbook). Here is an example: Excel equation: z = (Your Score (X)-Mean)/Standard Deviation) OR z = (X-Mean)/s. Z-score and probability calculation example o Assume Intelligent Quotient (IQ) scores are normally distributed with a Mean of 100 and Standard . Deviation of T5 o Assume a friend has an IQ score of 130 (X). o The z-score is then calculated: z (130 100)/15-30/15-2.00. Find Table A-2 in your textbook. The probability (green shaded area) associated with z -2.00 is p- 0.9772 o The probability of another friend scoring "higher" (non-shaded area) than 130 is: p (1.0000 0.9772) 0.0228 or 2.28%.

Answer 1

since the data is not in soft form ( as it is image ) so only using the column KC-135, for the first cell value=2.36 , following calculation is done and question is answered after feeding data into ms-excel.

here n=number of observation and population standard deviation is calculated using all the observation n=16

for for value of 2.36, z=(2.36-3.7831)/2.8718=-0.4956

P(Z<-0.4956)=0.3101 ( you can also use ms-excel command =normsdist(-0.4956))

following information has been generated using

Flight Name	KC-135
Stories 1	2.36
Stories 2	2.30
Stories 3
Stories 4	2.45
Stories 5	2.55
Stories 6	3.00
Stories 7	3.00
Stories 8	3.00
Stories 9	2.95
Stories 10	2.70
Stories 11	14.71
Stories 12	3.00
Stories 13	3.00
Stories 14	3.81
Stories 15	4.00
Stories 16	4.00
Stories 17	3.70
n=	16
sum=	60.5300
mean=	3.7831
standard deviation=	2.8718
Z-score value=	-0.4956
probability=	0.3101