Respuesta :
Given Information:
Mean test score = μ = 77
Standard deviation of test score = σ = 6.5 seconds
Answer:
The lower limit represents those 34% test scores which are below the mean test score.
The range of test scores will be (70.5 to 77)
The upper limit represents those 34% test scores which are above the mean test score.
The range of test scores will be (77 to 83.5)
Step-by-step explanation:
Normal Distribution:
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The Empirical Rule:
The empirical rule states that approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.
68% of all the data lie within 1 standard deviation from the mean, so that means 34% (half of 68%) of the test scores will be below the mean test score and remaining 34% of the test scores will be above the mean test score.
The confidence interval is given by
[tex]CI = \mu \pm 1 \cdot \sigma \\\\CI = 77 \pm 1 \cdot (6.5) \\\\CI = 77 \pm 6.5 \\\\Lower \: limit = 77 - 6.5 = 70.5 \\\\Upper \: limit = 77 + 6.5 = 83.5 \\\\[/tex]
The lower limit represents those 34% test scores which are below the mean test score.
So the range of test scores will be (70.5 to 77)
The upper limit represents those 34% test scores which are above the mean test score.
So the range of test scores will be (77 to 83.5)
