Question

Consider the density curve below:

[Diagram of a density curve]

Find the probability that the value is more than 2.

P(Z > 2) = [Provide the answer.]

Answer 1

To find P(Z > 2), subtract the area to the left of z = 2 (found in the z-table as 0.9772) from 1, which gives P(Z > 2) = 0.0228.

Step-by-step explanation:

The question asks to find the probability that a value is more than 2 for a standard normal distribution, denoted P(Z > 2). To calculate this probability, one can use a z-table, which provides the area under the standard normal curve to the left of a given z-score.

If you are dealing with a standard normal distribution, look up the z-score of 2 in the z-table to find the area under the curve to the left of 2. In most z-tables, this value is approximately 0.9772, which represents the probability that Z is less than 2. To find P(Z > 2), you subtract this value from 1 (because the total area under the curve is 1). Therefore, P(Z > 2) = 1 - 0.9772 = 0.0228.

Another approach is using technology such as a calculator's distribution functions, or statistical software, which can provide the probability directly.