I need help finding the IQR from the data given

Question

Use the Normal model

​N(1110,70) for the weights of steers.

​a) What weight represents the 58th ​percentile?

​b) What weight represents the 91st percentile?

​c) What's the IQR of the weights of these​ steers?

The 58th percentile is 1124.1 pounds

The weight representing the 91st percentile is 1203.9, I need to find the IQR for the weights of the steers is how many lbs?

 

 

Answer 1

In the normal model, m=1110lb (mean) and s=70lb (standard deviation).

Z=(X-m)/s=(X-1110)/70. We need Z for 0.25 (25th percentile) and 0.75 (75th percentile). Z for 0.75 is 0.675 so for 0.25 it’s -0.675 because of symmetry about the mean.

Therefore X=1110+70Z=1110+47.25. From the extremes of X we can calculate that the interquartile range is 2*47.25=94.5lb, between 1062.75 (Q1) and 1157.25 (Q3) pounds.

Yes, I agree that the 58th and 91st percentiles are about 1124.1 and 1203.9 pounds.