Sampling Distributions

ProfessorName
Paper
Date
ACES-II ejection seats were designed for men weighing between 140lb-211lb.Weights of
women are normally distributed with a mean of 143lb and a standard deviation of 29lb.
If a woman is randomly selected, the probability that her weight is between 140lb-211lb
will be as given below;
We calculate the z- score for a row value between 140 and 211.To decide on the
value, we can get the average of the two values as shown below;
Average of 140 and 211= 140+211=351/2=175.5=176.
Z-SCORE FOR 176= 176-143=33/29= 1.13793=1.14
Z-score = Row score – Mean
Standard Deviation

The z-score obtained has a positive value indicating that it is above the mean weight. If it
had a negative value ,it implies that it is below the mean weight.( “Analysis of microarray data using Z score transformation Cheadle, Chris, et al 73-81 .” 
From the z-score table P(Z=1.14)=0.8729.
If 36 women were selected, the probability that their weight will lie between 140 and
211lb will be given by ; 0.8729×36=31.4244
CONCLUSION
From the above two probabilities, the most relevant of the two will be the 0.8729.This is
because a valid probability is always equal to 1 or less than zero. To be able to calculate the
probabilities of the 36 women, we need to know the weight of each woman, calculate her z-score
and using the z-score table, we determine the probability of each.

Alternatively, we need to know
their weights, their mean weight and the standard deviation of their weights. From this
information, we can calculate the z-score and hence obtain the probability from the z-score table.
Probability of one means that there is a likely hood of an event to occur while as the probability
of zero means that there is the unlikely hood of an event occurring.

Notes
Z-score is a value that is used to standardize values in a data.
Standard deviation is a value that shows how far the value is from the mean.
Mean is a value that shows the average value of the data.

Work cited

Cheadle, Chris, et al. “Analysis of microarray data using Z score transformation.” The Journal of molecular diagnostics5.2 (2003): 73-81.