Asked by kenyana jones on May 15, 2024
Verified
A random variable x is normally distributed with a mean of 150 and a variance of 36. Given that x = 120, its corresponding z-score is 5.0.
Variance
A measure of dispersion in a set of data points, calculated by taking the average of the squared differences from the mean.
Standard Deviation
A statistic that quantifies the dispersion or variability of a dataset, measuring the average distance between each data point and the mean.
Z-score
A quantitative measure that demonstrates the correlation of a specific value to the mean of a dataset, identifying its separation from the mean by counting the standard deviations.
- Apply the properties of normal distributions to solve problems.
Verified Answer
KG
Kshama GuptaMay 16, 2024
Final Answer :
False
Explanation :
This statement is false. The given z-score of 5.0 suggests that x = 120 is unlikely under a normal distribution with mean 150 and variance 36. The actual z-score for x = 120 can be calculated as:
z = (120 - 150) / 6 = -5
Thus, the given z-score in the statement is incorrect.
z = (120 - 150) / 6 = -5
Thus, the given z-score in the statement is incorrect.
Learning Objectives
- Apply the properties of normal distributions to solve problems.