Asked by Nicole Salazar on Apr 27, 2024
Verified
If a distribution has a mean of 1,000 and a standard deviation of 100,how many standard deviations is 600 from the mean?
A) -2
B) -4
C) 4
D) 2
Mean
The arithmetic average of a set of values, calculated as the sum of all values divided by the total number of values.
Deviation
The amount by which a single measurement differs from a fixed value such as the mean or expected value.
- Assess and interpret deviations measured by standard deviations from the mean in a normal distribution.
Verified Answer
JB
Julie BemuyalMay 03, 2024
Final Answer :
B
Explanation :
To find how many standard deviations 600 is from the mean, we need to calculate the z-score:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation.
Plugging in the values, we get:
z = (600 - 1000) / 100 = -4
This means that 600 is 4 standard deviations below the mean. Therefore, the best answer choice is B, which corresponds to -4.
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation.
Plugging in the values, we get:
z = (600 - 1000) / 100 = -4
This means that 600 is 4 standard deviations below the mean. Therefore, the best answer choice is B, which corresponds to -4.
Learning Objectives
- Assess and interpret deviations measured by standard deviations from the mean in a normal distribution.