Find the value of the probability of the standard normal random variable z: (a) p (z<2.08) (b) p (z>1.87) (c) p (1.24<z<1.86) For a think it's just the value found on the standard normal distribution table right ? In this case 0.9812? For b is it 1 minus the z value? 1- 0.9693? For c I'm not so sure. Can someone explain the rules for this?
To find the value of the probability of the standard normal random variable z, you can use a standard normal distribution table (also called a z-table) or a statistical software.
(a) p(z < 2.08):
To find this value, you can use a standard normal distribution table. Look for the row corresponding to 2.0 and the column corresponding to 0.08. The intersection of this row and column gives you the cumulative probability up to 2.08. In this case, the value is approximately 0.9812.
(b) p(z > 1.87):
To find this value, you can use the same standard normal distribution table. However, the table usually provides cumulative probabilities up to a certain value, not beyond it. In this case, you can use the fact that the total area under the standard normal curve is 1. Therefore, you can find the probability of z being greater than 1.87 by subtracting the cumulative probability up to 1.87 from 1.
Cumulative probability up to 1.87 ≈ 0.9693.
Therefore, p(z > 1.87) = 1 - 0.9693 = 0.0307.
(c) p(1.24 < z < 1.86):
To find this value, you first find the cumulative probability up to 1.86 (let's call this A) using the z-table. Then, find the cumulative probability up to 1.24 (let's call this B). Finally, subtract the two probabilities to find the probability between them.
Cumulative probability up to 1.86 ≈ A.
Cumulative probability up to 1.24 ≈ B.
p(1.24 < z < 1.86) = A - B.
By using the standard normal distribution table, you can find A and B, and then subtract them to obtain the probability between the two values.