Question

Let z denote a variable that has a standard normal distribution. Determine each of the following probabilities:

a. P(z < 2.36)
b. P(z > 2.36)

Answer 1

The student's question involves finding probabilities for values under the standard normal distribution. P(z < 2.36) can be found using a Z-table, which provides the cumulative left-tail area. P(z > 2.36) is calculated by subtracting P(z < 2.36) from 1.

Step-by-step explanation:

The student is asking about calculating probabilities for a standard normal distribution (often denoted as Z). Specifically, the student wants to know:

1. The probability that the variable z is less than 2.36, is represented by P(z < 2.36).
2. The probability that z is greater than 2.36, represented by P(z > 2.36).

To answer these, you would typically use a standard normal table (Z-table), which provides the area to the left of a given z-value. For z = 2.36:

1. To find P(z < 2.36), you look up the value of 2.36 in the Z-table to find the cumulative area to the left. Let's say this is approximately 0.9909.
2. To find P(z > 2.36), you subtract the area found in part 1 from 1, since the total area under the curve is 1. So, P(z > 2.36) = 1 - P(z < 2.36) = 1 - 0.9909 = 0.0091.

However, without a Z-table or calculator at hand for this response, these probabilities are estimates based on typical values found in standard Z-tables.