Advanced level 2023 northwest regional mock pure mathematics with statistics 3
Advanced level 2023 northwest regional mock pure mathematics with statistics 3
(company of ii)the A shop bulbs Kstocks and from40company electrical % are from Dbulbs last company Ion*. D.nisknownthat a”30 dD%.Of ofthe thebulbs stock,from 60%company ofthe bui^K andTo 40V?
Findthe probability that abulb will last long.
(a) chosenat random fromthe s .
(b) chosen atrandom from the stoc wi S on8 or it is from companyK.
(c) that lasts long,chosen atrandom tron c will be from companyK.
2, A random variableX lias cumulative probnbility distribution function (3,3,2)marks
find tw=^ torx=1»L<3’4’5-6. /’*
(a) themeanofX.
(b) the variance ofX.
(c) P(x> 2)
. Jm<i
(ii)A studentis givenabundle ofkeysto open alock. Theprobability that akey selected atrandom will
open the lock is 17%. Given that different attempts at opening the lock are independent.
Find:
(a) the probabilitythatthe first key to openthe lock will be in his third attempt.
(b) the smallest integernforwhichthere willbe a95% chance ofopeningthe lock on or before the nth
attempt.
(3, 3)marks
3. The time taken by an air craft to fly over a city was measured by female students in upper sixth of a certain school
in the town. The results obtained were summarized in the table below
Time t(secs) 20-24 1 25-29 30-34 j 35-39 40-44 45-49 50-54 55-59
Number of students/ /2 2 8 8 16 13 9 10
Find,to two decimal places.
(a) the mean of the distribution.
(b) the standard deviation ofthe distribution
(c) the median ofthe distribution.
The 22 boysin the class measuredthe time independentofthe girls and obtained a mean time of20
seconds and a standard deviation of 8 seconds.
(d) Find,to two decimal places,the mean time and the variance ofthe time estimates made by the whole
class.
(3,3,2,5)mnrks
4. During Christmas, a balloon manufacturing company packaees balloons in packets whose weights are normally
distributed with mean 1kg and standard deviation 0.004kg. A packet of weight between 0.994kg and 1.006kgis
sold for 600FCFA. A packet of weight less than 0.99k<yi
than 1.006kg is sold lor 700FCFA.Find the probability that a packet ofballoons chosen at random from the
company’s production line has weight
(a) less than 0.99kg.
(b) between 0.994kg and1.006kg.
(c) greater than1.006kg
sold for 300FCFA while a packet of weight greater
The company produces 10.000 packets.Given thatthe cost ofproduction is 400 FCFA per packet,
(d)find the company’s expected profit trom the sales ofall the packets of balloons produced
