Aset of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. find the percent of data between 4.2 and 5.1.

To get the P(4.2≤x≤5.1) we proceed as follows:
z-score=(x-μ)/σ
where:
μ-mean
σ-standard deviation
when x=5.1
z-score=(5.1-5.1)/0.9=0
Thus
P(x≤5.1)=P(z≤0)=0.5000

when x=4.2
z-score=(4.2-5.1)/0.9=-1
P(x≤4.2)=P(z≤-1)=0.4602

Hence:
P(4.2≤x≤5.1)
=P(z≤0)-P(z≤-1)
=0.5-0.4602
=0.0398

0.0398

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