One deviation from the mean is 34% and since your answer is just one deviation from the mean, the answer is 34%
The percentage of scores lie between 80 and 86 is 34 % .
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
z = (x – μ) / σ
According to the question
Mean of the set of scores (μ)= 80
Standard deviation of the set of scores(σ)= 6.
and percentage of scores lie between 80 and 86 (x)
Now,
for 80
z score = (x – μ) / σ
= (80-80)/6 = 0
for 86
z score = (x – μ) / σ
= (86-80)/6 = 1
Therefore , value of z score for x will be between 0 to 1 .
Using normal distribution table , Probability that scores can be greater than 80 is
P(80<z) = 0.500
Probability that that scores can be less than 86 is
P(86>z) = 0.841
Now Probability that scores lie between 80 and 86
=> P(86>z) - P(80<z)
=> 0.841 - 0.500
=> 0.34
=> or 34%
Hence, percentage of scores lie between 80 and 86 is 34 % .
To know more about normal distribution and standard deviation and z score here :
https://brainly.com/question/13581723
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