Let Z~N(0, 1). Find a constant c for which

a. P(Z≥ c) = 0.1587

b. P(c ≤ Z ≤ 0) = 0.4772

c. P(‒c ≤ Z ≤ c) = 0.8664

d. P(0 ≤ Z ≤ c) = 0.2967

e. P(|Z| ≥ c) = 0.1470

Solution :

Step 1 of 5:

Given ZN(0,1)

Our goal is:

a). We need to find c, P(Zc)=0.1587

b). We need to find c, .

c). We need to find c, .

d). We need to find c,

e). We need to find c,

Now we have to calculate c value.

a).

Given, P(Zc)=0.1587.

Here we have to find c value.

P(Zc)=1-P(Zc)

P(Zc)=1-P(Zc)

P(Zc)= 0.1587

P(Zc)=1-0.1587

P(Zc)=0.8413

From the area under the normal table P(Z1)=0.8413.

Therefore c =1.