scores on a certain standardized test have a mean of 500, and a standard deviation of 100. how common is a…

scores on a certain standardized test have a mean of 500, and a standard deviation of 100. how common is a score between 600 and 700? calculate the probability.

scores on a certain standardized test have a mean of 500, and a standard deviation of 100. how common is a score between 600 and 700? calculate the probability.

Answer

Explanation:

Step1: Calculate z - scores

The formula for the z - score is (z=\frac{x-\mu}{\sigma}), where (\mu = 500) (mean) and (\sigma=100) (standard deviation). For (x = 600): (z_1=\frac{600 - 500}{100}=1) For (x = 700): (z_2=\frac{700 - 500}{100}=2)

Step2: Use the empirical rule (68 - 95 - 99.7 rule)

The empirical rule states that for a normal distribution:

  • Approximately (68%) of the data lies within (z=\pm1)
  • Approximately (95%) of the data lies within (z = \pm2)
  • Approximately (99.7%) of the data lies within (z=\pm3)

The proportion of data between (z = 1) and (z = 2) is (\frac{95% - 68%}{2})

[ \frac{95 - 68}{2}%=\frac{27}{2}% = 13.5% ]

Answer:

(13.5%)