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The scores from a state standardized test have a mean of 80 and a standard deviation of 10. The distribution of the scores is roughly bell shaped. to find the percentage of scores that lie between 60 and 80.

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Rau7star

Answer:

47.5%.

Step-by-step explanation:

60 is 2 standard deviations below the mean.

According to the emperical rule, there is approximately 90% of normally distributed  data within 2 standard deviations of the mean. Your interval is half of  that because it is the data between the mean and two standard deviations

below the mean. therefore, the answer is 47.5%.

raphealnwobi

The percentage of scores that lie between 60 and 80 is 47.75%

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation[/tex]

Given that:

μ = 80, σ = 10

[tex]For\ x=60:\\\\z=\frac{60-80}{10} =-2\\\\For\ x=80:\\\\z=\frac{80-80}{10} =0[/tex]

P(60 < x < 80) = P(-2 < z < 0) = P(z < 0) - P(z < -2) = 0.5 - 0.0228 = 47.75%

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