Question

3.1.45 Use the Normal model N(1127,72) for the weights of steers. a) What weight represents the 31st percentile? b) What weight represents the 93rd percentile? c) What's the IQR of the weights of these steers? a) The weight representing the 31st percentile is (Round to the nearest whole number as needed.) pounds. Enter your answer in the answer box and then click Check Answer. parts remaining

Answer 1

Solution:-

Given that,

mean = $\mu$ = 1127

standard deviation = $\sigma$ = 72

a) Using standard normal table,

P(Z < z) =31 %

= P(Z < z) = 0.31  

= P(Z < -0.50) = 0.31

z = -0.50

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = -0.50 * 72 + 1127

x = 1091

31 st percentile is = 1091

b) Using standard normal table,

P(Z < z) =93 %

= P(Z < z) = 0.93

= P(Z < 1.48) = 0.93  

z = 1.48

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.48 * 72 + 1127

x = 1233.56

93 rd  percentile is = 1234

c) The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.67 ) = 0.25

z = -0.67

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = -0.67 * 72 + 1127

x = 1078.76

First quartile =Q1 = 1079

The z dist'n Third quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.67 ) = 0.75

z = 0.67

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 0.67 * 72 + 1127

x = 1175.24

Third quartile =Q3 = 1175

IQR = Q3 - Q1

IOR = 1175 - 1079 = 96