Asked by Elodie Charlorin on May 15, 2024
Verified
A continuous random variable x is normally distributed with a mean of 100 oz. and a standard deviation of 20 oz. Given that x = 120, its corresponding z-score is -1.0.
Z-score
A standardized score that indicates how many standard deviations a data point is from the mean.
Continuous Random Variable
A variable that can assume an infinite number of values within a given range, where the outcomes cannot be counted but are measured.
- Calculate and interpret Z-scores in the context of normally distributed data.
Verified Answer
TA
Tyson AndersonMay 16, 2024
Final Answer :
False
Explanation :
The z-score is calculated as z=x−μσz = \frac{x - \mu}{\sigma}z=σx−μ , where xxx is the value in question, μ\muμ is the mean, and σ\sigmaσ is the standard deviation. Plugging in the given values, z=120−10020=1z = \frac{120 - 100}{20} = 1z=20120−100=1 , not -1.
Learning Objectives
- Calculate and interpret Z-scores in the context of normally distributed data.