Answer to Question #299768 in Statistics and Probability for dwarfy

Question

He wants to know how to identify the regions under the normal curve corresponding to different standard normal values. Your friend will send a picture of a normal curve with the corresponding area, and he asks you favor to explain each picture on how to obtain the value of the shaded part of the normal curves. Here is the screenshot of the

pictures.

the first image is P(z>2.19) , probability is 11.7%

second image P(-2.56<z<1.96), probability is 96.98%

Answer 1

the first image is P(z>2.19)

P(z>2.19 is defined as 1 - p(z<2.19)

using the normal table, we obtain p(z<2.19) = 0.98574

taking 1- 0.98574 = 0.01426

second image P(-2.56<z<1.96), probability is 96.98%

using the normal table we obtain z score of -2.56 = 0.00523

using the normal table, we also obtain z score of 1.96= 0.97500

Thus P(-2.56<z<1.96) = (0.97500 - 0.00523) = 0.96977