CA Foundation · Quantitative Aptitude · Theoretical Distributions
The heights of a large group of students are normally distributed. It is known that 15.87% of students are taller than 170 cm, and 2.28% are taller than 180 cm. (Use: area from 0 to Z=1 is 0.3413 and from 0 to Z=2 is 0.4772.) What are the mean and standard deviation of the heights?
The mean is 160 cm and the standard deviation is 10 cm. An upper tail of 15.87% corresponds to Z = 1 and 2.28% to Z = 2, so 170 and 180 are one and two standard deviations above the mean, giving a 10 cm SD and mean 160.
- AMean 160 cm, SD 10 cmCorrect
- BMean 165 cm, SD 5 cm
- CMean 150 cm, SD 20 cm
- DMean 170 cm, SD 10 cm
Explanation
P(Z > z) = 0.1587 gives z = 1, so (170 - mean)/SD = 1. P(Z > z) = 0.0228 gives z = 2, so (180 - mean)/SD = 2. Subtracting: 10/SD = 1, so SD = 10 and mean = 160. Check: 165 and 5 gives Z = 1 for 170 but Z = 3 for 180, which fails.
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