Find the value of z0.025.

Question

Accepted Answer

Welcome back, everyone. Calculate the Z score that marks the cutoff for the top 10% of the standard normal distribution. A says 1.28, B 1.65. C 1.96. In the 2.33. So basically what we can do in this problem is visualize the standard normal distribution. We have our bell-shaped curve, and essentially we're looking for the cutoff for the top 10%, right? We can mark it off. Let's suppose that we have a value for the top 10, right? So, essentially it means that we have a Total of 0.10 area below the curve from. Some Z lowercase c, right? And essentially because the total area below the curve is 1, we can see that the remaining area below the curve is 1 minus 0.10, right? So essentially our area in pink. is equal to 1 minus 0.10, which is 0.90. And now we have to recall that the probability of Z being less than lowercase z in this context is 0.90. Basically, it tells us that if Z is less than lowercase z, then the area is equal to 0.90. And now what we can do is simply use this equation and use the inverse normal function to determine the lowercase z value. Additionally, we can use the tables and we can simply identify the area of 0.90. So the Z score for that. Either using a table or an inverse normal function is going to be 1.28, and that will be our final answer which corresponds to the answer choice A. Thank you for watching.

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