A.) What weight represents the 66th percentile? B.) What weight represents the 9

Question

A.) What weight represents the 66th percentile? B.) What weight represents the 96th percentile? C.) what's the IQR of the weights of these steers? Use the Normal model N(1105,52) for the weights of steers. a) What weight represents the 66th percentile? b) What weight represents the 96th percentile? c) What's the IQR of the weights of these steers? a) The weight representing the 66th percentile is pounds. Round to the nearest whole number as needed.) b) The weight representing the 96th 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.) Enter your answer in each of the answer boxes

Explanation / Answer

Solution:

We are given

Distribution is normal.

Mean = 1105

SD = 52

Part a

Here, we have to find 66th percentile.

X = mean + Z*SD

Z for 66th percentile = 0.412463

(by using z-table)

X = 1105 + 0.412463*52

X = 1126.448

Required 66th percentile = 1126

Part b

We have to find 96th percentile.

X = mean + Z*SD

Z for 96th percentile = 1.750686

(by using z-table)

X = 1105 + 1.750686*52

X = 1196.036

Required 96th percentile = 1196

Part c

We have to find IQR

IQR = Q3 – Q1

Q3= 75th percentile

Q1 = 25th percentile

75th percentile = 1105 + 0.67449*52

75th percentile = 1140.073

25th percentile = 1105 - 0.67449*52

25th percentile = 1069.927

IQR = Q3 – Q1

IQR = 1140.073 - 1069.927

IQR = 70.146

IQR = 70 approximately

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