Question

Determine the probability of having an error between

a) -1.1 σ and +1.5 σ

b) -2.1 σ and 0 σ

for a normal variable.

[20%) II. Probability for Normal distribution Determine the probability of having an error between a)-1.1 σ and +1.5 σ b)-21 σ and 0 σ for a normal variable. Use Table D.1 from the lecture notes for the standard normal distribution calculations, or use Excel functions.

Answer 1

Answer:

Determine the probability of having an error between

1. -1.1 σ and +1.5 σ

Using standard normal distribution,

we have to find P( -1.1<z<1.5)

= P( z <1.5)-P( z < -1.1)

Excel function: =NORM.S.DIST(1.5,TRUE) -NORM.S.DIST(-1.1,TRUE)

Answer: =0.7975

2. -2.1 σ and 0 σ

we have to find P( -2.1<z<0)

= P( z <0)-P( z < -2.1)

= 0.4821

Excel function: =NORM.S.DIST(0,TRUE) -NORM.S.DIST(-2.1,TRUE)

c).

area under the curve –infinity to 1.68

= P( z < 1.68)

= 0.953521

Excel function: =NORM.S.DIST(1.68,TRUE)