Answer to Question #336696 in Statistics and Probability for felicity

Question #336696

Given πœ‡ = 45, and 𝜎 = 5.5. (7 points)

a. What is the raw score when 𝑧 = βˆ’1.57?


b. What is the raw score when 𝑧 = 2.09?


c. What is the raw score when βˆ’0.48 < 𝑧 < 1.4?


d. What is the raw score when βˆ’2.17 < 𝑧 < 1.79? e. What is the raw score when 𝑧 = 0.09?


1
Expert's answer
2022-05-04T12:04:12-0400

a.


z=xβˆ’ΞΌΟƒ=βˆ’1.57z =\dfrac{x-\mu}{\sigma}= βˆ’1.57

x=45βˆ’1.57(5.5)=36.365x=45-1.57(5.5)=36.365

b.


z=xβˆ’ΞΌΟƒ=2.09z =\dfrac{x-\mu}{\sigma}= 2.09

x=45+2.09(5.5)=56.495x=45+2.09(5.5)=56.495

c.


z=xβˆ’ΞΌΟƒ=βˆ’0.48z =\dfrac{x-\mu}{\sigma}= βˆ’0.48

x=45βˆ’0.48(5.5)=42.36x=45-0.48(5.5)=42.36




z=xβˆ’ΞΌΟƒ=1.4z =\dfrac{x-\mu}{\sigma}= 1.4


x=45+1.4(5.5)=52.7x=45+1.4(5.5)=52.7

42.36<x<52.742.36<x<52.7

d.


z=xβˆ’ΞΌΟƒ=βˆ’2.17z =\dfrac{x-\mu}{\sigma}= βˆ’2.17

x=45βˆ’2.17(5.5)=33.065x=45-2.17(5.5)=33.065




z=xβˆ’ΞΌΟƒ=1.79z =\dfrac{x-\mu}{\sigma}= 1.79


x=45+1.79(5.5)=54.845x=45+1.79(5.5)=54.845

33.065<x<54.84533.065<x<54.845

e.


z=xβˆ’ΞΌΟƒ=0.09z =\dfrac{x-\mu}{\sigma}= 0.09

x=45+0.09(5.5)=45.495x=45+0.09(5.5)=45.495


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