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Question

The mean height of 385 students is 163 cm,the standard deviation is 10 cm. Assuming that the heights are normally distributed,what percent of the height are greater than 170 cm and how many students having a height between 155 cm and 165 cm?

Answer 1

Want to find P(x > 170)

x is N(163,10)

z = (x - mean)/SD is N(0,1)

P(x > 170) = P(z > (170 - 163)/10) = P(z > 0.7) = P(z < -0.7) = 0.2420

First find P(155 < x < 165)

= P((155-163)/10 < z < (165-163)/10) = P(-0.8 < z < 0.2) = P(z < 0.2) - P(z < -0.8) = 0.5793 - 0.2119 = 0.3674

To find how many students: 385 * 0.367= 141.449 ~ 141