A normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95% of the observations will occur. In the book it says that the answer is X=56.60, but I have no clue how they got that.
A normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95% of the observations will occur. In the book it says that the answer is X=56.60, but I have no clue how they got that.
u know mean (μ) =50 and s.d (σ) =4
1-∝=95%
now according to normal dist"-
Z=[(x-μ)/σ ]~N(0,1)
using porbabily p(Z<1.645)=0.95
p((x-50)/4<1.645)=0.95
by simplifing p(x<56.58)=0.95
therefore x=56.58 when value below 95%of observations occur.
P.S: 1.645 is a table value if u take it as 1.65 u get answer as 56.60
hope it would help u..
thank u
amul