The z-score of the given values are a measure of how many standard
deviations are between the given value and the mean.
The proportion of students that own between 20 and 30 pairs of shoes is
0.5256
Reasons:
The mean score, [tex]\bar{x}[/tex] = 22.1
Standard deviation of the sample, s = 6.3
The range of the shoe size = Between 20 and 30
The z-score, is given as follows;
[tex]Z= \mathbf{\dfrac{x-\mu }{\sigma }}[/tex]
The z-score of 30 is given as follows;
[tex]Z=\dfrac{30-22.1 }{6.3 } \approx 1.254[/tex]
The probability from the z-table is, P(x < 30) = 0.89507
The z-score of 20 is given as follows;
- [tex]Z=\dfrac{20-22.1 }{6.3 } \approx -0.333[/tex]
Therefore, from the z-table, we have;
P(x < 20) = 0.36944
∴ The difference P(20 < x < 30) = 0.89507 - 0.36944 = 0.52563
P(20 < x < 30) ≈ 0.5256
The proportion of students that own between 20 and 30 pairs of shoes is
0.5256.
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