Homework SourseFind the following probabilities based on a standard normal
| Find the following probabilities based on a standard normal variable Z. Use Table 1. (Round your answers to 4 decimal places.) |
| a. | P(Z > 0.74) | |
| b. | P(Z 1.92) | |
| c. | P(0 Z 1.62) | |
| d. | P(0.90 Z 2.94) | |
| Find the following probabilities based on a standard normal variable Z. Use Table 1. (Round your answers to 4 decimal places.) |
Solution
a)
Using a table/technology, the right tailed area of this is
P(z > 0.74 ) = 0.2296 [ANSWER]
****************
b)
Using a table/technology, the left tailed area of this is
P(z < -1.92 ) = 0.0274 [ANSWER]
*********************
c)
z1 = lower z score = 0
z2 = upper z score = 1.62
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.5
P(z < z2) = 0.9474
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.4474 [ANSWER]
*********************
d)
z1 = lower z score = -0.9
z2 = upper z score = 2.94
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.1841
P(z < z2) = 0.9984
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.8143 [ANSWER]
