Solution:
Value of z = σx−xˉ
Value of z corresponding to the first group of items under 10% = 0.5 – 0.1 = 0.4
0.4 on the table = - 0.6554
Z = σx−xˉ
-0.6554 = σ50−xˉ
−0.6554σ=50−xˉ
xˉ−0.6554σ=50
Value of z corresponding to the second group of items under 90% = 1 – 0.9 = 0.1
0.1 on the table = 0.5398
Z = σx−xˉ
0.5398= σ90−xˉ
0.5398σ=90−xˉ
xˉ+0.5398σ=90
Solve for the system equations:
xˉ−0.6554σ=50
xˉ+0.5398σ=90
−1.1952σ=−40
σ=33.47
The value of the standard deviation in the distribution = 33.47
Substitute the value of σ in the first equation to derive x̅:
xˉ−0.6554σ=50
xˉ−0.6554(33.47)=50
xˉ−21.94=50
xˉ=50+21.94=71.94
xˉ=71.94
The value of the mean of the distribution = 71.94
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