Question

Use the Normal model ​N(1178​,89​) for the weights of steers. ​a) What weight represents the 64th ​percentile? ​b) What weight represents the 93rd ​percentile? ​c) What's the IQR of the weights of these​ steers?

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 1178

S.d = 89

A)

From z table, P(z<0.36) = 64%

0.36 = (x - 1178)/89

X = 1210.04

B)

From z table, P(z<1.48) = 93%

1.48 = (x - 1178)/89

X = 1309.72

C)

IQR = Q3 - Q1

We know that below Q3, 75% lies

From z table, P(z<0.67) = 75%

0.67 = (Q3 - 1178)/89

Q3 = 1237.63

Below Q1, 25% lies

From z table, P(z<-0.67) = 25%

-0.67 = (Q1 - 1178)/89

Q1 = 1118.37

IQR = 1237.63 - 1118.37 = 119.26