Statistic I question

Question

Use the Normal model N(1103​,82​) for the weights of steers.

​a) What weight represents the 42nd ​percentile?

​b) What weight represents the 97th percentile?

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

Answer 1

Use z-score formula z - (x - mean)/standard deviation, where x = weight, 1103 = mean and 82 = SD.

so z = (x - 1103)/82

a) Look up z closest to 0.42 probability, then plug that value in for z in formula and solve for x.

b) Look up z closest to 0.97 probability, then plug that value in for z in formula and solve for x.

c) IQR is 75th percentile - 25th percentile

Look up z closest to 0.75 and 0.25 probabilities, then plug those values into z in formula for solve for x values then take the difference of those x values.