Question

For a Normal distribution with mean, μ

=

2

μ=2

, and standard deviation, σ

=

4

σ=4

,

10% of observations have a value less than  Round to 4 decimal places.

10% of observations have a value greater than  Round to 4 decimal places.

Answer 1

N(2; 16) = 2 + 4N(0,1)

1). We have to find such value a that P(2 + 4N(0,1) < a) = 0.1

$P(2 + 4N(0,1) < a)=0.1\to P(N(0,1)<{\frac {a-2} 4})=0.1\to {\frac {a-2} 4} = -1.2816\to$

$\to a=-3.1264$

10% of observations have a value less than -3.1264

2). We have to find such value b that P(2 + 4N(0,1) > b) = 0.1

$P(2 + 4N(0,1) >b)=0.1\to P(N(0,1)>{\frac {b-2} 4})=0.1\to {\frac {b-2} 4} = 1.2816\to$

$\to b=7.1264$

10% of observations have a value greater than 7.1264