Question

Use the normal model N (1193, 63) for the weights of steers.

A) what weight represent the 32nd percentile?

B) what weight represents the 98th percentile?

C) what’s the IQR of the weights of these steers?

Round to the nearest whole number as needed.

Answer 1

A)

mu= 1193

sigma= 63

X= unknown

probability= 0.32

z-score for probability=-0.4677

Z=(X-mu)/sigma

x=(mu+Z*sigma)

X=1193-0.4677*63

x= 1163.534976

rounded is 1164

B)

mu= 1193

sigma= 63

X= unknown

probability= 0.98

z-score for probability=2.0537

Z=(X-mu)/sigma

x=(mu+Z*sigma)

X=1193+2.0537*63

x= 1322.386

Rounded is 1322

C)

IQR= weight for 75 percentile - weight for 25 percentile

Weight for 25 percentile

mu= 1193

sigma= 63

X(25)= unknown

probability= 0.25

z-score for probability=-0.6744

Z=(X-mu)/sigma

x(25)=(mu+Z*sigma)

=1193-0.6744*63

x(25)=1150.507

Weight for 75 percentile

mu= 1193

sigma= 63

X(75)= unknown

probability= 0.75

z-score for probability=0.6745

Z=(X-mu)/sigma

x(75)=(mu+Z*sigma)

=1193+0.6745*63

x(75)= 1235.492

IQR=1235.492-1150.507

=84.985

IQR rounded =85

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