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)=cnr.pr.qn−rP(X=7)=C107(0.6)7(0.4)3 =0.0860(ii)P(X≤7)=1−P(X>7)=1−P(X=8)−P(X=9)−P(X=10)=1−C108(0.6)8(0.4)2−C109(0.6)9(0.4)1−C1010(0.6)10(0.4)0=1−0.1209−0.0403−0.0060=0.8328
(b)(i)P(X>V)=30.5%P(Z>V−95016)=0.305P(Z>0.51)=0.305 V−95016=0.51V=0.51(16)+950 =958.16 cm3
(ii)Probability=P(930<X<960)=P(930−95016<Z<960−95016)=P(−1.25<Z<0.625)=1−P(Z>1.25)−P(Z>0.625)=1−0.1056−0.2660=0.6284
(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.
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2018/08/Picture24.png)
(i) the value of V,
(ii) the probability that the volume between 930 cm3 and 960 cm3.
Solution:
(a)(i)P(X=r)=cnr.pr.qn−rP(X=7)=C107(0.6)7(0.4)3 =0.0860(ii)P(X≤7)=1−P(X>7)=1−P(X=8)−P(X=9)−P(X=10)=1−C108(0.6)8(0.4)2−C109(0.6)9(0.4)1−C1010(0.6)10(0.4)0=1−0.1209−0.0403−0.0060=0.8328
(b)(i)P(X>V)=30.5%P(Z>V−95016)=0.305P(Z>0.51)=0.305 V−95016=0.51V=0.51(16)+950 =958.16 cm3
(ii)Probability=P(930<X<960)=P(930−95016<Z<960−95016)=P(−1.25<Z<0.625)=1−P(Z>1.25)−P(Z>0.625)=1−0.1056−0.2660=0.6284