Answer to Question #217721 in Statistics and Probability for qianhe

Question

Topic: Normal Distribution Distribution & Inverse Normal Distribution

1.) The value of  P( -1.96 < Z < 1.96 ) is                        .  

A. 0.9000

B. 0.9500

C. 0.9900

D. 0.9990

2.) The area under a normal curve between 0 and -1.75 is __________.

           A. 0.0401

           B. 0.9599

           C. 0.4599

           D. None of the above

Answer 1

1.

where Z ~ N(0, 1).

This is equal to P(Z < 1.96) - P(Z < -1.96)

= F(1.96) - F(-1.96) = F(1.96) - (1 - F(1.96)) = 2 F(1.96) - 1

Now we need to look in a table to find out what F(1.96) is.

If you look in statistical tables for the standard normal distribution,

To find F(1.96), read across the 1.9 line until you get to 6 (for 1.96). So F(1.96) = 0.975 .

Hence P(-1.96 < Z < 1.96) = 2 × 0.975 - 1 = 0.95 .

2.

P(-1.75<z<0)

= P(0<z<1.75)

= 0.4599