Apps. and Interpretation for IBDP Maths Ebook 1 | Page 296

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 83
1. A box holds 80 apples. The probability that an apple is rotten is 0.06. Let X be the
number of rotten apples in the box.
(a)
(b)
(c)
Find the expected number of rotten apples in the box.
Find the probability that there are exactly 10 rotten apples in the box.
Find the probability that there are at least 15 rotten apples in the box.
[2]
[2]
[3]
2. In a school the probability that a student is left-handed is 0.12. A sample of 135 students
is randomly selected from the school. Let X be the number of left-handed students in the
sample.
(a)
(b)
(c)
Find the expected number of left-handed students in this sample.
Find the probability that exactly 20 students are left-handed.
Find the probability that more than 16 students are left-handed.
[2]
[2]
[3]
3. A factory makes lamps. The probability that a lamp is defective is 0.02. The factory tests
a random sample of 50 lamps. Let X be the number of defective lamps in the sample.
(a)
(b)
(c)
Find the mean number of defective lamps in the sample.
Find the probability that there are exactly nine defective lamps in the sample.
Find the probability that there is at most two defective lamps in the
sample.
[2]
[2]
[2]
4. The probability of obtaining heads on a biased coin is 0.69. The coin is tossed nine times.
(a)
(b)
(c)
Find the mean number of heads.
Find the probability of obtaining exactly six heads.
Find the probability of obtaining less than three heads.
[2]
[2]
[2]
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