Asked by Rachel Wiechelman on May 29, 2024
Verified
Given a normal distribution with a mean of 80 and a standard deviation of 20, an observation of x = 50 corresponds to a standard normal deviate:
A) of z = +1.5
B) of z = +3.0
C) of z = -1.5
D) of z = -3.0
E) of none of these
Standard Normal Deviate
Another term for Z-score, highlighting its role in standard normal distribution.
Standard Deviation
Standard deviation is a measure used in statistics to quantify the amount of variation or dispersion of a set of values.
Normal Distribution
A symmetrical, bell-shaped distribution of data where most of the observations cluster around the central peak and the probabilities of values taper off equally in both directions from the center.
- Evaluate probabilities relevant to the standard normal distribution (z-scores).
Verified Answer
CF
Candace FlakesJun 01, 2024
Final Answer :
C
Explanation :
To find the standard normal deviate, we use the formula z = (x - μ) / σ, where x is the observation, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (50 - 80) / 20 = -1.5. Therefore, the answer is choice C.
Learning Objectives
- Evaluate probabilities relevant to the standard normal distribution (z-scores).