Answer:
15.9% of the data will be greater than 235.3.
Step-by-step explanation:
Use a calculator with statistical functions. In this case you'll need the cumulative normal distribution: normcdf(.
Evaluate the following: normcdf(235.3, 10000,186.4, 48.9):
We get: 0.159, or 15.9%
15.9% of the data will be greater than 235.3.
The range of value X > 284.2 of data will be greater than 235.3.
A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores.
We know that the upper 2.5% of data would be 97.5% of data.
We will use a z-score formula to solve our given problem.
[tex]\rm z=\dfrac{x-\mu}{\sigma}[/tex]
Where; z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
We will use a normal distribution table to find a z-score corresponding to 97.5% area or 0.975.
We can see from the normal distribution table that the z-score corresponding to the area of 0.975 is 1.96.
[tex]\rm 1.96=\dfrac{x-186.4}{48.9}\\\\1.96 \times 48.9 =x-186.4\\\\x = 186.4 +95.84\\\\x=282.84[/tex]
Hence, the range of value X > 284.2 of data will be greater than 235.3.
Learn more about z-score here;
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