Question

Suppose that the scores for an exam were known to be normally distributed with a mean of 150. If the 90th percentile score was 170 , what would the standard deviation be? (Use the tables.) 6.1254

11.25
15.625
19.5
22
25.1542
28.25
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None of these Question 21 (6.25 points) Suppose that the weight of a particular breed of steer are ∼N(1152,84). What is the IQR of the weights of this breed of steer? (Use calculator function.) 98.25
113.31
185.54
225.25
285.65
310.05
333.41
​
None of these

Answer 1

Explanation:

(a)

μ = 150

P(X<170) = 0.9 → Ф(X<170) = 1.282

`Z=(x-\mu)/(\sigma)`

`1.282=(170-150)/(\sigma)`

`\sigma=(20)/(1.282)`

= 15.6

(b)

μ = 1152

σ² = 84

σ = √84

P(X<x₁) = 0.25 (Q1) → Ф(X<x₁) = -0.674

`Z=(x-\mu)/(\sigma)`

`-0.674=(x1-1152)/(√(84) )`

`x1=-0.674√(84) +1152`

= 1145.82

P(X<x₂) = 0.75 (Q3) → Ф(X<x₂) = 0.674

`Z=(x-\mu)/(\sigma)`

`0.674=(x1-1152)/(√(84) )`

`x2=0.674√(84) +1152`

= 1158.18

IQR = x₂ - x₁

= 1158.18 - 1145.82

= 12.36