First we should declare our known variables: (population mean) µ = 70in, (population s.d.) σ = 3in.
- Let's remember the equation for the Z statistic: Z = (x-µ)/σ
- Make sure you have a Z distribution chart to reference
a. Actor Michael B. Jordan is 6’0” (72”) tall. What percentage of adult men are shorter than Michael?
Z = (72-70)/3 = .67 (round to two decimal places because most Z dist. charts only round to two)
The corresponding value on the table is .74857 which can be read in this context as the probability of an adult man having a height of 0-72 inches, and no greater.
Answer is 74.857%
b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?
Z = (67-70)/3 = -1
The corresponding value is .15866 which can be read in this context as the probability of an adult man having a height of 0-67 inches, and no greater. But since we are concerned with the percentage of those taller than jack, we take the compliment of .15866, which is (1 – .15866 = .84134).
Answer is 84.134%