Long Questions (Question 10)


Question 10:
(a) It is found that 60% of the students from a certain class obtained grade A in English in O level trial examination.
If 10 students from the class are selected at random, find the probability that
(i) exactly 7 students obtained grade A.
(ii) not more than 7 students obtained grade A.

(b) Diagram below shows a standard normal distribution graph representing the volume of soy sauce in bottles produced by a factory.

It is given the mean is 950 cm3 and the variance is 256 cm6. If the percentage of the volume more than V is 30.5%, find
(i) the value of V,
(ii) the probability that the volume between 930 cm3 and 960 cm3.

Solution:
(a)(i) P(X=r)= c n r . p r . q nr P(X=7)= C 10 7 ( 0.6 ) 7 ( 0.4 ) 3    =0.0860 ( ii ) P(X7) =1P(X>7) =1P( X=8 )P( X=9 )P( X=10 ) =1 C 10 8 ( 0.6 ) 8 ( 0.4 ) 2 C 10 9 ( 0.6 ) 9 ( 0.4 ) 1 C 10 10 ( 0.6 ) 10 ( 0.4 ) 0 =10.12090.04030.0060 =0.8328

(b)( i ) P( X>V )=30.5% P( Z> V950 16 )=0.305 P( Z>0.51 )=0.305    V950 16 =0.51 V=0.51( 16 )+950    =958.16  cm 3

( ii ) Probability =P( 930<X<960 ) =P( 930950 16 <Z< 960950 16 ) =P( 1.25<Z<0.625 ) =1P( Z>1.25 )P( Z>0.625 ) =10.10560.2660 =0.6284