4. The mean height of a large population of university students is 172 cm with a standard deviation of 10.8 cm. The rand

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4. The mean height of a large population of university students
is 172 cm with a standard deviation of 10.8 cm. The random variable
X refers to the heights of students in this population. That is, X
~ N( μ = 172, σ = 10.8).
(a) P( X < 155) = ?
(b) P( X = 170) = ?
(c) P( X > 160) = ?
(d) P( 165 < X < 190) = ?
(e) What proportion of this population is either shorter than
150cm or taller than 185cm?
(f) In this population, how unusual is it for a student to be
taller than 2 metres? Quantify your answer.
(g) How short/tall is a student who is 1.6 standard deviations
away from the mean height?
(h) What range of heights contains the middle half of this
distribution?