Question

The heights of 1000 students are normally distributed with a mean of 174.5 cm and a standard deviation of 6.9 cm. Assuming that the heights are recorded to the nearest quarter-centimeter down, how many of these students would you expect to have heights greater than or equal to 188 cm?

Answer 1

Z multiplier

$Z=(x-\mu)/\sigma$

Z=(188-174.5)/6.9

Z=1.96

Probability correspondin to Z=1.96 is 0.9750

Probability corresponding height greater than x=188cm is

1-0.9750=0.025

Expected number=np=1000x0.025=25