As per the standard distribution, the lowest test score is 27.76%
Standard distribution:
In statistics, standard distribution means a normal distribution with a mean of zero and standard deviation of 1.
Given,
The top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12.
Here we need to find the lowest test score that still qualifies for a scholarship.
As per the given question, we have identified the value of
=> μ = 76 (mean)
=> σ = 12 (standard deviation)
Then we need to take the value of x as,
x < 5% (find the probability)
Now, converting the problem in standard form
=> Z = (5 − 76) / 12
=> Z = -5.91
Then as per the z table the value is 0.2786
To know more about standard distribution here.
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