(f) Assume the height of a student is normally distributed, with mean
μ
1
, variance
σ
2
1
for
boys, and mean
μ
2
, variance
σ
2
2
for girls. The heights of 9 randomly selected students
were measured to be 1.72, 1.76, 1.80, 1.65 m for males, and 1.56, 1.48, 1.62, 1.55, 1.58 m
for females.
(g) A sample of size 5 is drawn at random without replacement from a population of size
N
= 2000, in which there are
m
males and
N

m
females and
m
is not known. It is
found that there is only one male in the selected sample.
(h) An icemaking machine produces ice cubes of nominal volume 1 cm
3
. Assume the actual
volume of an ice cube produced is normally distributed with mean 1 cm
3
and variance
σ
2
.
In a production run, volumes of 8 ice cubes were measured as follows (in cm
3
): 0.82, 1.01,
1.03, 0.92, 0.84, 1.10, 0.78, 0.93.
A random sample of size 100 was found to consist of 3 red, 24 yellow, 30 brown and 43
(j) Flaws appear at random on sheets of a certain type of photographic paper, so that the
number of ﬂaws on a single sheet follows a Poisson (
λ
) distribution. On 6 separate sample
sheets, 12, 2, 4, 6, 5 and 10 ﬂaws were detected respectively.
2.