6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find the z-score corresponding to the probability/area shown under the standard normal curve below.
A
-1.52
B
1.52
C
0.82
D
-0.82
Verified step by step guidance1
Understand that the problem is asking for the z-score corresponding to a given area under the standard normal curve. The area provided is 0.9357.
Recall that the standard normal distribution is symmetric around 0, and the total area under the curve is 1. The area to the left of a z-score represents the cumulative probability.
Since the area to the left of the z-score is 0.9357, you need to find the z-score such that the cumulative probability is 0.9357.
Use a standard normal distribution table (z-table) or a calculator with statistical functions to find the z-score that corresponds to a cumulative probability of 0.9357.
Look up the value in the z-table or use the calculator to find that the z-score corresponding to a cumulative probability of 0.9357 is approximately 1.52. Since the area is to the right of the mean, the z-score is positive.
9:47mWatch next
Master Finding Standard Normal Probabilities using z-Table with a bite sized video explanation from Patrick
Start learning
