Question

in order to find a 95% confidence interval we need to find values aa and bb such that for Z?N(?=0,?=1),Z?N(?=0,?=1),

P(a<Z<b)=0.95.P(a<Z<b)=0.95.

(a) Suppose a=?2.1556.a=?2.1556. Then b=b= ____ .

(b) Suppose b=2.2044.b=2.2044. Then a=a= ____ .

any help would be greatly appreciated

Answer 1

We are given that:

(a)

Now, we are given that a = -2.1556

=> P(Z<b) - P(Z<-2.1556) = 0.95

=> P(Z<b) - 0.015557 = 0.95

=> P(Z<b) = 0.965557

From the table of standard normal distribution, we find : P(Z<1.8192) = 0.965557

Thus, b = 1.8192

(b)

Now, we are given that b = 2.2044

=> P(Z<2.2044) - P(Z<a) = 0.95

=> 0.986252 - P(Z<a) = 0.95

=> P(Z<a) = 0.036252

From the table of standard normal distribution, we find : P(Z<-1.7959) = 0.036252

Thus, a = -1.7959

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