Multiple Choice
For the standard normal distribution, what -value corresponds to a lower-tail probability of ?
13
views
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
In a perfectly normal distribution of scores, what percentage of the data falls within of the mean ?
A
B
C
D
Verified step by step guidance1
Recall that a perfectly normal distribution is symmetric and follows the empirical rule, which describes the percentage of data within certain standard deviations from the mean.
The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
To find the percentage of data within one standard deviation, focus on the interval from \(\mu - \sigma\) to \(\mu + \sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.
Understand that this interval captures the central portion of the distribution where most data points lie, reflecting the natural variability around the mean.
Therefore, the percentage of data within one standard deviation of the mean in a normal distribution is approximately 68%.
9:47mWatch next
Master Finding Standard Normal Probabilities using z-Table with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Standard Normal Distribution practice set
Problem sets built by lead tutorsExpert video explanations