EXERCISES IN STATISTICS
Series A, No. 4
1. Ten jurors are selected at random from a long list of names of which one
third belong to women. The selection is regarded as unsatisfactory if either
sex is represented by less than three people. Find the probability that the
selection will be unsatisfactory.
Answer:
The probability of a juror being a woman is 1
/
3. The number
x
of
the women on the jury has a binomial distribution:
x
∼
b
(
x, n
=10
,p
=
1
3
)
.
The selection is unsatisfactory if
x
∈{
0
,
1
,
2
,
8
,
9
,
10
}
, and the probability of
this event is
b
(0) +
b
(1) +
b
(2) +
b
(8) +
b
(9) +
b
(10)
=
±
2
3
¶
10
+10
±
1
3
¶±
2
3
¶
9
+
10
×
9
2
±
1
3
¶
2
±
2
3
¶
8
+
10
×
9
2
±
1
3
¶
8
±
2
3
¶
2
+10
±
1
3
¶
9
±
2
3
¶
+
±
1
3
¶
10
=
17
,
856
59
,
049
’
3
10
.
2. Assume that the distribution of the heights of adult males is approximately
normal with a mean of 69 ins and a standard deviation of 3 ins. What is
the conditional probability that an individual will be taller than 72 ins if
it is known that he is taller than 70 ins.?
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 Spring '12
 D.S.G.Pollock
 Normal Distribution, Probability, Probability theory, series A, diﬀerent mixedsex pairs

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