Question 4 Suppose a student’s pocket money (inclusive of part-time salary), fol

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Question 4 Suppose a student’s pocket money (inclusive of part-time salary), follows a normal distribution with mean RM900 and standard deviation of RM23. a)Are the listed variables above a parameter or statistics?(1m) b)Calculate the probability that a student’s income (i)is exactly RM1100(1m) (ii)is more than RM1200(2m) (iii)is between RM 850 and RM1200(3m) (iv)is between RM850 and RM1200, given that this student has more than RM800(3m) Question 4 Suppose a student’s pocket money (inclusive of part-time salary), follows a normal distribution with mean RM900 and standard deviation of RM23. a)Are the listed variables above a parameter or statistics?(1m) b)Calculate the probability that a student’s income (i)is exactly RM1100(1m) (ii)is more than RM1200(2m) (iii)is between RM 850 and RM1200(3m) (iv)is between RM850 and RM1200, given that this student has more than RM800(3m) Question 4 Suppose a student’s pocket money (inclusive of part-time salary), follows a normal distribution with mean RM900 and standard deviation of RM23. a)Are the listed variables above a parameter or statistics?(1m) b)Calculate the probability that a student’s income (i)is exactly RM1100(1m) (ii)is more than RM1200(2m) (iii)is between RM 850 and RM1200(3m) (iv)is between RM850 and RM1200, given that this student has more than RM800(3m)

Explanation / Answer

a)as above represent for population hence they are parameter,

b) for normal distribution z=(X-mean)/std deviation

(i)as normal distribution is continuous , it will give probabilty for interval while for point estimate probability =0

hence probabilty for exactly RM1100=0

(ii)P(X>1200)=1-P(X<1200)=1-P(Z<(1200-900)/23) =1-P(Z<13.4)=1-1=0

(iii) P(850<X<1200)=P(-2.1739<Z<13.4)=1-0.0149=0.9851

(iv)P(X>800)=1-P(X<800)=1-P(Z<-4.3478)=1-0=1

hence P(850<X<1200|X>800)=0.9851/1=0.9851

i have a doubt that std deviation should be 230.

please revert.

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