CIE Oct 2020 9709 Prob & Stats 2 Paper 62 (pdf)
- On average, 1 in 50 000 people have a certain gene.
Use a suitable approximating distribution to find the probability that more than 2 people in a random
sample of 150 000 have the gene.
- A six-sided die has faces marked 1, 2, 3, 4, 5, 6. When the die is thrown 300 times it shows a six on
(a) Calculate an approximate 96% confidence interval for the probability that the die shows a six on
(b) Maroulla claims that the die is biased.
Use your answer to part (a) to comment on this claim
- A random variable X takes values between 0 and 3 only and has probability density function as shown
in the diagram, where c is a constant.
(a) Show that c = 2/3
(b) Find P(X > 2)
(c) Calculate E(X)
- The areas, X cm2, of petals of a certain kind of flower have mean μ cm2
. In the past it has been found
that μ = 8.9. Following a change in the climate, a botanist claims that the mean is no longer 8.9. The
areas of a random sample of 200 petals from this kind of flower are measured, and the results are
∑x = 1850,
∑x2 = 17 850.
Test the botanist’s claim at the 2.5% significance level.
- Customers arrive at a shop at a constant average rate of 2.3 per minute.
(a) State another condition for the number of customers arriving per minute to have a Poisson
It is now given that the number of customers arriving per minute has the distribution Po(2.3).
(b) Find the probability that exactly 3 customers arrive during a 1-minute period
(c) Find the probability that more than 3 customers arrive during a 2-minute period
(d) Five 1-minute periods are chosen at random. Find the probability that no customers arrive during
exactly 2 of these 5 periods.
- A biscuit manufacturer claims that, on average, 1 in 3 packets of biscuits contain a prize offer. Gerry
suspects that the proportion of packets containing the prize offer is less than 1 in 3. In order to test the
manufacturer’s claim, he buys 20 randomly selected packets. He finds that exactly 2 of these packets
contain the prize offer.
(a) Carry out the test at the 10% significance level.
(b) Maria also suspects that the proportion of packets containing the prize offer is less than 1 in 3.
She also carries out a significance test at the 10% level using 20 randomly selected packets. She
will reject the manufacturer’s claim if she finds that there are 3 or fewer packets containing the
Find the probability of a Type II error in Maria’s test if the proportion of packets containing the
prize offer is actually 1 in 7.
(c) Explain what is meant by a Type II error in this context.
- Before a certain type of book is published it is checked for errors, which are then corrected.
purposes each error is classified as either minor or major. The numbers of minor and major errors in
a book are modelled by the independent distributions N(380, 140) and N(210, 80) respectively. You
should assume that no continuity corrections are needed when using these models.
A book of this type is chosen at random.
(a) Find the probability that the number of minor errors is at least 200 more than the number of
The costs of correcting a minor error and a major error are 20 cents and 50 cents respectively.
(b) Find the probability that the total cost of correcting the errors in the book is less than $190
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