dult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of 3.5357 (to 4 decimal places)

Answer 1

the underlying formula that you want to use here is

Z = (x - mean) / (standard deviation)

for this scenario that means taking

3.5357 = (x - 69) / 2.8

x = 3.5357(2.8) + 69

x = 78.9

so the height of a man with that Z score is 78.9 inches

Answer 2

z = (x - µ) / σ where:

1. z = z-score
2. x = observed value (height of a man)
3. σ = population standard deviation (standard deviation of the heights)
4. µ = population mean (mean heights)

Since we're given z-score, the population mean, and the population standard deviation, all that's left to solve for is x, the height of a man with corresponding z-score of 3.5357.

3.5357 = (x - 69.0) / 2.8

x = 78.9000 inches

Hope this was helpful.