1. Let be the mean of the distribution ofX and > 0 the standard deviation of the
ID: 3044290 • Letter: 1
Question
1. Let be the mean of the distribution ofX and > 0 the standard deviation of the distribution of X. It follows that The population inner quartile range (IQR) is define as xo2s-x 7. The population IOR is a measure of variability. Observe that Define the population lower fence (LF) and population upper fence (UF) by Note, LF = x075-1.5×IOR and UF = x025 + 1.5 x 10R. If X has a normal distribution, the proportion of individuals in the population whose X measurement falls between the LF and the UF is (A) normalcdfu-4 * invNorm(0.75) * , + 4 * invNorm (0.75) * ,,) (B) normalcd-4invNorm(0.75),4 * invNorm(0.75)) (C) 0.9930232988 (D) all of theseExplanation / Answer
as for 0.25 and 0.75 critical values of z are z0.25 ;z0.75
as due to symmetry ; z0.25 = -z0.75
therefore IQR =1.5*(z0.75-z0.25)=1.5*2*z0.75 =3*z0.75
hence UF = z0.75 +3*z0.75 =4*z0.75
and LF =z0.25 -3*z0.75 =-4*z0.75
as P(-4*z0.75 <Z<4*z0.75 ) =0.993024
hence all of above option is correct
option D is correct .
please revert for any clarification required
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