Sampling Distributions

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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 ; 0.8729x36=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.

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