j2 revision exercises on sampling & estimation set a

8/11/2019 J2 Revision Exercises on Sampling & Estimation Set A

1/5

Temasek JC 2009 JC 2 Mathematics H2 9740

J2 Revision Exercises: Sampling & Estimation (SetA)

1 The publisher of a magazine that is sold at newsstands wants to investigate which sectionof the magazine is most popular among the readers. Explain whether it is possible to

obtain a random sample of the magazines readership.

The publisher obtained a sample by inviting readers to fill in their favourite section in aform printed in one issue of the magazine and to send it to the publisher. Postage is freeand a small token is given for readers who respond. State one reason why this methodmay be unsatisfactory.

Explain how the publisher can take a uota sample of the magazines readers whopurchase the magazines from newsstands. !"##$%Prelim%&'S%P"%()

2 * country club has +### members of which $## are males and "## are females. Theirnames are recorded in a computer system in alphabetical order. The committee of the

club wishes to find out the type of activities preferred by the members and conducts asurvey on +## members of the club.

(i) Explain how a systematic sampling method can be used to select these +## members.

(ii) ,ive one advantage and one disadvantage of this method.(iii) Suggest a method of obtaining a more representative sample and describe how it may

be carried out. !"##$%Prelim%TP-%"%(

3 There are ++ hospitals in Singapore that offer stomach banding surgery. To investigate theeffectiveness of stomach banding surgery in Singapore/ a postgraduate student decides to

conduct a survey with +## patients who had undergone stomach banding surgery at0ational 1niversity 'ospital. Explain why this sample is biased.2t is known that the number of patients who had undergone stomach banding surgery ineach hospital is different. &escribe how the postgraduate student should obtain a morerepresentative sample of +## patients in order to determine the effectiveness of stomach

banding surgery in Singapore.!"##$%P-%P")

4 The student population of "/3## in a 4unior college is made up of male and femalestudents who are either in -+ or -" as follows5

-+ Students -" Students

6ale 73# (3#

8emale 33# 33#

* sample of 3# students is to be taken from the population to investigate the numberof hours of sleep a student from this 4unior college has on average per night.

(a) State and describe in detail a suitable method of sampling.

(b) The students are now listed in alphabetical order and they are numbered from + to"3## consecutively. * number between + and 3#/ inclusive/ is selected at random.

The corresponding student and every 3#

th

student thereafter are included in thissample.

(i) 2dentify this method of sampling.

1


2/5


(ii) ,ive an advantage of using the method of sampling you have described in (a)rather than this method of sampling. !#7%Prelim%9-%"%:)

2


3/5


5 *n employer has commissioned an opinion polling organisation to undertake a survey ofstaff responses to the proposed changes in the pension scheme. The staff are categorisedas management/ professional and administrative/ and it is thought that there might beconsiderable differences of opinion among the categories. There are (#/ +;# and eave youranswers to " decimal places.

(iv)8ind the probability that the mean salary of (# people taken at random is more than?imit Theorem to estimate the approximate probability that the sum of

3# independent observations of X is greater than the sum of +## independentobservations of Y.State precisely where in your solution you have made use of the entral >imit Theorem.

!0F-%"##(P22%C


4/5


10 * certain type of plant is known to attract two species of caterpillars/ * and G. Thenumber of each type of caterpillar on the plant is independent of the other type and eachfollows a Poisson distribution with mean " and < respectively.

(i) Show that the probability that a randomly chosen plant has more than the expectednumber of caterpillars on it is #.ake &istrict and offers bed and breakfast to visitors. *t breakfast/visitors help themselves to orange 4uice. 'e observes that the total amount of orange

4uice reuired by visitors at each breakfast may be modelled by a normal distributionwith mean +;(# ml and standard deviation ;## ml.

(a) &afydd keeps the orange 4uice in a fridge in +### ml cartons.

8ind the probability that at a particular breakfast5

(i) one full carton of orange 4uice will be sufficient to meet the visitorsreuirementsH

(ii) two/ but not more than two/ full cartons of orange 4uice will be needed to meetthe visitors reuirements.

(b) The mean amount of orange 4uice reuired by visitors at the 7 breakfasts in a

particular week is denoted by X .

(i) State the distribution of X. *ssume that the reuirement for orange 4uice at

each breakfast is independent.

(ii) 8ind the value of X which is exceeded in +B of weeks.

(iii) 'ow many full cartons of orange 4uice must &afydd have in his fridge/ at thebeginning of a particular week/ to ensure that the probability of being able tomeet the visitors reuirements for that week/ without replenishing his supplies/is at least #.::A

(c) &afydd also provides grapefruit 4uice at breakfast. 'e observes that at "$B ofbreakfasts more than +### ml of grapefruit 4uice is reuired. The amount ofgrapefruit 4uice reuired may be modelled by a normal distribution with mean mland standard deviation


5/5


12 *n aptitude test for deep=sea divers produces scores which are normally distributed on ascale from # to +##. * random sample of +(# divers were assessed/ and each of theirindividual test scores/x/ was recorded. The results are summarized by

( )"

:+"#/

j2 revision exercises on sampling & estimation set a

Documents