Answer :
Answer:
a) x < 30 = z < 0.65
b) 19 < x = -1.91 < z
Or x > 19 = z > -1.91
c) 32 < x < 35 = 1.12 < z < 1.81
Step-by-step explanation:
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - xbar)/σ
x = the value to be standardized, that is, converted to z-score
xbar = mean = 27.2 kg
σ = standard deviation = 4.3 kg
a) For x < 30
We standardize the 30 kg weight first
z = (x - xbar)/σ = (30 - 27.2)/4.3 = 0.65
x < 30 = z < 0.65
b) For 19 < x
We standardize the 19 kg weight first
z = (x - xbar)/σ = (19 - 27.2)/4.3 = - 1.91
19 < x = - 1.91 < z
Or x > 19 = z > - 1.91
c) For 32 < x < 35
We standardize the 32 kg and 35 kg weights first
z = (x - xbar)/σ
z₁ = (32 - 27.2)/4.3 = 1.12
z₂ = (35 - 27.2)/4.3 = 1.81
32 < x < 35 = 1.12 < z < 1.81
The conversion of the respective x-intervals to z-intervals are; z < 0.65; z > -1.91; 1.12 < z < 1.81
What is the z-interval?
The formula for z-score is;
z = (x - x')/σ
where;
x = the value that is converted to z-score
x' is the mean = 27.2 kg
σ is standard deviation = 4.3 kg
a) We want to convert x < 30 to z-interval;
Z-score is;
z = (30 - 27.2)/4.3
z = 0.65
Thus, the z-interval of x < 30 is; z < 0.65
b) We want to convert x > 19 to z-interval;
Z-score is;
z = (19 - 27.2)/4.3
z = - 1.91
Thus, the z-interval of x > 19 is z > -1.91
c) We want to convert 32 < x < 35 to z-interval;
z-score for x = 32 is;
z₁ = (32 - 27.2)/4.3
z₁ = 1.12
z-score for x = 35
z₂ = (35 - 27.2)/4.3
z₂ = 1.81
Thus, the z - interval for 32 < x < 35 is 1.12 < z < 1.81
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