Answer:
a.) 0.468
b.) -0.075
c.) 0
Explanation:
Given the distribution :
Z~N(μ = 0,σ = 1)
Distribution = normal
Mean (μ) = 0
Standard deviation (σ) = 1
a) Find x so that P(Z ≤ x) = 68%
Using the z probability calculator : Zscore corresponding to 68% = 0.68 = 0.468
Usingbthe relation :
Zscore = (x - m) / σ
0.468 = (x - 0) / 1
0.468 = x - 0
x = 0.468
b) Find the data value x at the 47th percentile
47th percentile = Zscore of - 0.075
Zscore = (x - m) / σ
-0.075 = (x - 0) / 1
-0.075 = x - 0
x = -0.075
c) Find the data value x at the 50th percentile
50th percentile = Zscore of 0.0
Zscore = (x - m) / σ
0.0 = (x - 0) / 1
0.0 = x - 0
x = 0