79.5k views
0 votes
The expression P(z>-2.05) represents the area under the standard normal curve above a given

value of z.
Use your standard normal table to find the indicated area. Use a sketch of the standard normal
curve with the appropriate are a shaded to help find the answer.
What is the value of P?
Express your answer rounded to 4 decimal places.

User Namuna
by
8.6k points

1 Answer

5 votes

Final answer:

To find P(z>-2.05), use a z-table to find the area to the left of -2.05, and then subtract this value from 1. Sketching the standard normal curve and shading the area right of z=-2.05 can help visualize the calculated probability.

Step-by-step explanation:

The student is asking to calculate the probability that a randomly chosen value from a standard normal distribution is greater than -2.05, denoted as P(z>-2.05). To find this value, we generally use a z-table, which indicates the area under the curve to the left of a given z score. To find P(z>-2.05), we would look up the value of -2.05 in the z-table and find the corresponding area to the left of z. Most z-tables provide this left-tail area directly.

So, suppose the z-table shows the area to the left of -2.05 as 0.0202 (just an example, not the actual value). The area to the right, which represents P(z>-2.05), is given by 1 minus the left-tail area. So we calculate P(z>-2.05) = 1 - 0.0202 = 0.9798.

To give a visual representation, one can sketch a standard normal distribution curve, shade the area to the right of z=-2.05, and label the shaded area with the calculated probability.

User ChristianM
by
7.8k points