SOLUTION: I am stumped with these two problems. Can someone assist please and if possible, show your workings? 1. Suppose that Z is a n(0,1) variable. Which of the following statements

Question 421212: I am stumped with these two problems. Can someone assist please and if possible, show your workings?
1. Suppose that Z is a n(0,1) variable. Which of the following statements is incorrect?
a. P(Z > 2.6) = P(Z < -2.6)
b. P(-0.8 < Z < 1.4) = 1 - P(Z > 1.4) - P(Z < -0.8)
c. P(Z > -2.8) = P(Z < 2.8)
d. P(Z < 0.74) = P(Z < -0.74)
e. P(Z > 0.0 = P(Z < 0.0)
2. Of Z~n(0,1) with P(a < Z < 1.8) = 0.7800. What is the value of a?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Suppose that Z is a n(0,1) variable. Which of the following statements is incorrect?
a. P(Z > 2.6) = P(Z < -2.6)
True: the area of the right tail = the area of the left tail.
----------------------------------------------------
b. P(-0.8 < Z < 1.4) = 1 - P(Z > 1.4) - P(Z < -0.8)
True: the inbetween area = the whole area - the tails' areas.
-----------------------------------------------------
c. P(Z > -2.8) = P(Z < 2.8)
True: the right tail above -2.8 = the left tail below 2.8
---------------------------------------------------------
d. P(Z < 0.74) = P(Z < -0.74)
False: these two left tails are not equal
-----------------------
e. P(Z > 0.0 = P(Z < 0.0)
True: Each probability is 1/2
----------------------------------
2. Of Z~n(0,1) with P(a < Z < 1.8) = 0.7800. What is the value of a?
Assume (1/2)(0.7800) = 0.3900 is between z = 0 and z=1.8
---
Find the z-value with a left tail of 0.5-0.39 = 0.11
a = invNorm(0.11) = -1.2265
=====================
Cheers,
Stan H.

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