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Z score and raw score conversion

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Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that x has an approximately normal distribution with mean μ = 6.8 hours and standard deviation σ = 2.1 hours.

Convert each of the following x intervals to standardized z intervals:
a) x ≤ 7.5
b) 5 ≤ x ≤ 8
c) x ≥ 4.

Convert each of the following z intervals to raw score x intervals:
d) z ≥ -2
e) 0 ≤ z ≤ 2
f) z ≤ 3 .

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The solution gives the details of conversion between z score and raw score.

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