High School

In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is approximately normal with a mean of 528 and a standard deviation of 117.

What proportion of students earned scores between 500 and 600 on the SAT math test?

Round your answer to 4 decimal places.

Answer :

Around 34.07% of students earned scores between 500 and 600 on the SAT math test in the class of 2019.

The desired range = 500 to 600

The mean of the distribution = 528

Standard deviation = 117

Calculating the standardized scores -

[tex]z = (x - u) / a[/tex]

For the lower bound of 500:

z1 = (500 - 528) / 117

= -28/117

= -0.2393

For the upper bound of 600:

z2 = (600 - 528) / 117

= 72/117

= 0.6153

Using a standard normal distribution table to determine the cumulative probabilities associated with z-scores.

[tex]P(500 < X < 600) = P(z1 < Z < z2)[/tex]

Calculating -

[tex]P(z1 < Z < z2) = P(-0.2393 < Z < 0.6154)[/tex]

As per the table,

P(-0.2393 ≤ Z ≤ 0.6154) is around 0.3407.

Read more about scores on:

https://brainly.com/question/29969863

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