Question

1) In order to find a 89% confidence interval we need to find values a and b such that for Z ~ N (mu=0, sigma=1), P(a<Z<b)=0.89.

(a) Suppose a= -2.8418. Then b=____?

(b) Suppose b=2.036. Then a=____?

Answer 1

If we need to find the p value using excel, we use NORMSDIST(Z value) and if we want to get the Z value, then use the excel formula NORMSINV(p value). We can also use online technology, or z tables, but most z tables give us values correct to 2 decimal places.

__________________________________________________________________________________

Given = 0 and = 1

Z = (X - )/

P(a < Z < b) = P(Z < b) - P(Z < a) = 0.89

(a) Given a = -2.8418

Therefore P(Z < -2.8418) Using technology, [(NORMSDIST(-2.8418) ] = 0.0022

Therefore P(Z < b) = 0.89 + 0.0022 = 0.8922

Therefore b (Using technology, [(NORMSINV(0.8922)]) = 1.2383

_______________________________________________________________________________

(b) Given b = 2.036

Therefore P(Z < 2.036) Using technology [(NORMSDIST(2.036) ] = 0.9791

Therefore P(Z < a) = 0.9791 - 0.89 = 0.0891

Therefore a (Using technology, [(NORMSINV(0.0891)]) = -1.3463

______________________________________________________________________________