Question

In order to find a 90% confidence interval we need to find values aa and bb such that for Z∼N(μ=0,σ=1),Z∼N(μ=0,σ=1),

P(a<Z<b)=0.9.

(a) Suppose a=−2.5562.a=−2.5562. Then b=

(b) Suppose b=2.9501.b=2.9501. Then a=

Answer 1

By using online calculator, trying different values of b to get 0.9 area [for (a) by fixing a =−2.5562] and trying different values of a to get 0.9 area [for (b) by fixing b =2.9501].

(a)

P(−2.5562 < Z < 1.3125) =0.9

Therefore, b =1.3125

(b)

P(-1.2905 < Z < 2.9501) =0.9

Therefore, a = -1.2905

By using the table of "Area under Standard Normal Curve", it is solved as follows: