Use the Normal model N(1144, 73) for the weights of steers. a) What weight repre

Question

Use the Normal model N(1144, 73) for the weights of steers. a) What weight represents the 51st percentile? b) What weight represents the 97th percentile? c) What's the IQR of the weights of these steers? a) The weight representing the 51st percentile is pounds. (Round to the nearest whole number as needed.) b) The weight representing the 97th percentile is pounds. (Round to the nearest whole number as needed.) c) The IQR for the weights of these steers is pounds. (Round to the nearest whole number as needed.)

Explanation / Answer

a) z score for 51st percentile = 0.025

Hence,

Weight representing 51st percentile = 1144 + 0.025 (73) = 1146

b) z score for 97th percentile = 1.88

Hence,

Weight representing 97th percentile = 1144 + 1.88(73) = 1281

c) IQR = Q3 - Q1

z score for 75th percentile = 0.67

z score for 25th percentile = -0.67

So,

IQR = (1144 + 0.67(73) - (1144 - 0.67(73)

IQR = 98

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