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A teacher wanted to know how well the gifted students in here class perform relative to her other classes. She administers a standardized test with a mean of 50 and a standard deviation of 10. A student scores of 55, what percent of students have a higher score than hers

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JeanaShupp

Answer: 30.85%.

Step-by-step explanation:

Let X denotes the score of  random student.

Given: [tex]\mu = 50[/tex] and [tex]\sigma=10[/tex]

We assume that scores are normally distributed.

Then , the probability that a a student score higher than 55:

[tex]P(X>55)=P(\dfrac{X-\mu}{\sigma}>\dfrac{55-50}{10})\\\\=P(Z>0.5) \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.5)\\\\=1-0.6915\ [\text{By p-value table for z}]\\\\= 0.3085[/tex]

Hence, the percent of students have a higher score than hers is 30.85%.

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