CA Foundation · Quantitative Aptitude · Theoretical Distributions
The heights of a large group of students are normally distributed. If 15.87% of students are taller than 170 cm and 15.87% are shorter than 150 cm, what are the mean and standard deviation of the heights? (Use the fact that P(Z > 1) = 0.1587.)
The mean is 160 cm and the standard deviation is 10 cm. Equal tail areas place the mean midway between 150 and 170, and since a 15.87% upper tail corresponds to Z = 1, 170 lies one standard deviation, 10 cm, above the mean.
- AMean 160 cm, standard deviation 5 cm
- BMean 160 cm, standard deviation 10 cmCorrect
- CMean 160 cm, standard deviation 20 cm
- DMean 165 cm, standard deviation 10 cm
Explanation
Equal tails of 15.87% mean 170 and 150 are symmetric about the mean, so mean = (170 + 150)/2 = 160. P(Z > 1) = 0.1587 means 170 is one standard deviation above the mean, so sigma = 170 - 160 = 10. Standard deviation 5 would treat the points as two sigma away, which is wrong.
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