Find The Probability Of Z Using The Standard Normal Distribu…

Find the probability of z using the standard normal distribution.
1. P(0<z<1.49)
2. P(-1.52<z<1.43)
3. P(-1.45<z<0)
4. P(z>1.97)
5. P(z<-1.29) ​

Answer:

Here are the solutions for finding probability using the standard normal distribution:

1. P(0

0 < z < 1.49

z = 0.7465 (mid-point)

P(z < 0.7465) = 0.4652 (using normal distribution table)

P(0 < z < 1.49) = 0.4652

2. P(-1.52

-1.52 < z < 1.43

z = -0.045 (mid-point)

P(z < -0.045) = 0.4753 (using normal distribution table)

P(-0.045 < z < 0.945) = 0.4897 (subtracting from 1)

P(-1.52

3. P(-1.45

-1.45 < z < 0

z = -0.725 (mid-point)

P(z < -0.725) = 0.2419 (using normal distribution table)

P(-0.725 < z < 0) = 0.7581 (subtracting from 1)

P(-1.45

4. P(z>1.97)

z > 1.97

P(z > 1.97) = 0.9772 (using normal distribution table)

5. P(z<-1.29)

z < -1.29

P(z < -1.29) = 0.0995 (using normal distribution table)

P(z < -1.29) = 0.0995

Let me know if you need more details or have any other questions! I can also provide examples for additional problems involving the standard normal distribution.

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