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The scholastic assessment test is standardized to be normally distributed with a mean μ=500 and a standard deviation σ=100. What percentage of SAT scores falls
a. between 500 and 600
b. between 400 and 600
c. between 500 and 700
d. between 300 and 700
e. above 600
f. below 300

Respuesta :

Manetho

Answer:

68.27%.

Step-by-step explanation:

Here we have [tex]\mu=500,\sigma=100[/tex]

Let X shows the SAT score. z-score for X=400 is

[tex]z=\frac{X-\mu}{\sigma}=\frac{400-500}{100}= -1[/tex]

z-score for X=600 is

[tex]z=\frac{X-\mu}{\sigma}=\frac{600-500}{100}=1[/tex]

So the proportion of SAT scores falls between 400 and 600 is

[tex]P(400<X<600)=P(-1<z<1)=0.6827[/tex]

hence, required percentage is 68.27%.

one can use the same method to find the% for all other cases as

well.

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