the mean is 100, standard deviation is 16. what is the % of scores between 52 and 148?
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To find the percentage of scores between 52 and 148, given a mean of 100 and a standard deviation of 16, we can use the properties of the normal distribution.
1. Start by calculating the z-scores for the given values using the formula:
z = (x - μ) / σ,
where x is the value, μ is the mean, and σ is the standard deviation.
For 52:
z = (52 - 100) / 16
= -3
For 148:
z = (148 - 100) / 16
= 3
2. Look up the z-scores in the standard normal distribution table or use a calculator to find the corresponding cumulative probability values. The cumulative probability represents the percentage of scores below a given z-score.
For z = -3, the cumulative probability is approximately 0.0013.
For z = 3, the cumulative probability is approximately 0.9987.
3. Calculate the percentage of scores between 52 and 148 by subtracting the cumulative probabilities:
Percentage = (0.9987 - 0.0013) * 100
= 0.9974 * 100
= 99.74%
Therefore, approximately 99.74% of the scores fall between 52 and 148 in the given distribution.