Find the value of p, if the mean of the following distribution is 20.


x:



15



17



19



20+p



23



y:



2



3



4



5p



6



X



y



yx



15



2



30



17



3



51



19



4



76



20 + p



5p



100p + 5p2



23



6



138




N = 5p + 15



yx = 295 + 100p + 5p2



Given,


Mean = 20


= 20


= 20


295 + 100p + 5p2 = 100p + 300


295 + 5p2 = 300


5p2 = 300 – 295


5p2 – 5 = 0


5 (p2 – 1) = 0


p2 – 1 = 0


(p + 1) (p – 1) = 0


p = 1


If p + 1 = 0, p = - 1 (Reject)


Or p – 1 = 0, p = 1


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