Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than 70% of the students who took the test. What should Tom's score at least be in order to be admitted.
NOTE: WRITE YOUR ANSWER USING 4 DECIMAL DIGIT. FOR EXAMPLE 0.1234 OR 3.2450. DO NOT ROUND UP OR DOWN THE LAST DECIMAL DIGIT.
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Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.70) in larger portion and its Z score. Insert the Z score in the above equation to find the score.
so the equation would be..
.7580=(x-500)/100
but i'm not getting a clear answer.
To determine Tom's score, we need to find the cutoff score that corresponds to the top 70th percentile of the test scores.
To do this, we can use the Z-score formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.
First, we need to find the Z-score corresponding to the 70th percentile. Since the normal distribution is symmetric, we can find this value by subtracting 0.70 from 1 (to get 0.30) and referring to the Z-table or using a statistical calculator.
From the Z-table or calculator, we find that the Z-score corresponding to the 70th percentile is approximately 0.5244.
Now, we can solve for the raw score (X) using the Z-score formula: X = Z * σ + μ.
Plugging in the values, we have: X = 0.5244 * 100 + 500 = 552.44.
Thus, Tom's score should be at least 552.44 to be admitted to the university.
Therefore, the answer is 552.4400.