Stats Doubt

[Tanushree]

 One more doubt.. with normal distribution

Q) In a Normal Distribution, 31% of the items are under 45 and 8% over 64. Find Mean and Standard Deviation

ii) What % of the items differ from the mean by a number not more then 5?

Ans: for 1) Let X denote the variable under consideration. Then we have,
P(X<45) =0.31 and P(X> 64)= 0.08

If X has normal distribution with mean and standard deviation , then the standard deviation to X=45 and X=64 then,
Z= 45 - Mean/SD -z1

When X=64, Z=64-Mean/SD
P( 0<Z< z2)= 0.42--------------------   z2 = 1.405 ( from table) (( <b>Where is 1.405 , I cannot find it anywhere)   while 0.19 in the table is 0.0753 while in the SC gupta book its given 0.496.. Am I going wrong.

Guys if anyone has SC . Gupta Stats book please refer to 14.52,14.53 pages... Need you help..

[mrittik]

I think u r right...but for this problem normal table is needed....is it so?

[Granpa Simpson]

Tanushree for this problem u will have to find out the values of Z1 and Z2 corresponding to the areas 0.19 and 0.42..watever u are finding out is the area under the circumstance that u know Z1 and Z2..but in this case z1 and Z2 are unknown..u dont need to find the area under the curve rather u will have to find the points Z1 and Z2 corresponding to the given area..in that case z1=-0.49 and z2=1.41.