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Answer :
The proportion of students who have their scores between 400 and 700 points will be between 0.7745 and 0.9772.
Scores on the college admissions test are approximately normally distributed with a mean of 500 and a standard deviation of 100. The normal distribution is a continuous probability distribution that is symmetric around its mean.
To determine the proportion of students who have their scores between 400 and 700 points, we need to calculate the area under the normal curve within this range. This can be done by standardizing the scores and using the Z-table or a statistical software.
Standardize the scores:
To standardize a score, we subtract the mean and divide by the standard deviation.
For 400 points:
Z-score = (400 - 500) / 100 = -1
For 700 points:
Z-score = (700 - 500) / 100 = 2
Find the cumulative probability:
Using the Z-table or statistical software, we can find the cumulative probability associated with the Z-scores.
For a Z-score of -1, the cumulative probability is approximately 0.1587.
For a Z-score of 2, the cumulative probability is approximately 0.9772.
Calculate the proportion:
The proportion of students between 400 and 700 points is the difference between the two cumulative probabilities:
Proportion = 0.9772 - 0.1587 = 0.8185
Therefore, we can affirm that the proportion of students who have their scores between 400 and 700 points will be between 0.7745 and 0.9772.
Learn more about proportion
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