Question

For each of the following problems, identify the correct distribution and find the probabilities: (a) X∼N(0,1);P(X>.25 or X<−.3)

Answer 1

The correct distribution for the problem is the standard normal distribution, represented by X ~ N(0,1). The probability that X > 0.25 or X < -0.3 is 0.4013, the probability that X < -0.3 is 0.3821, and the probability that -0.3 < X < 0.25 is 0.2166.

Step-by-step explanation:

The correct distribution for the problem is the standard normal distribution, which is represented by X ~ N(0,1). To find the probabilities, we need to calculate the area under the curve of the standard normal distribution.

1. First, we need to find the area to the right of 0.25. We can do this by subtracting the area to the left of 0.25 from 1. Using a z-table or a calculator, we find that the area to the left of 0.25 is approximately 0.5987. Therefore, the area to the right of 0.25 is 1 - 0.5987 = 0.4013.
2. Next, we need to find the area to the left of -0.3. Using a z-table or a calculator, we find that the area to the left of -0.3 is approximately 0.3821.
3. To find the area between -0.3 and 0.25, we subtract the area to the left of -0.3 from the area to the left of 0.25. Using the values we calculated in the previous steps, we find that the area between -0.3 and 0.25 is 0.5987 - 0.3821 = 0.2166.

Therefore, the probabilities are as follows: P(X > 0.25 or X < -0.3) = 0.4013, P(X < -0.3) = 0.3821, and P(-0.3 < X < 0.25) = 0.2166.