Question

Mathematics achievement test scores for 500 students were found to have a mean and a variance equal to 510 and 3600, respectively. If the distribution of test scores was mound-shaped, approximately how many of the scores would fall into the interval 450 to 570? (Round your answer to the nearest whole number.) scores

Approximately how many scores would be expected to fall into the interval 390 to 630? (Round your answer to the nearest whole number.)

scores

Answer 1

P(450 < X < 570)

$= P(\frac{450-510}{\sqrt{3600}} < z < \frac{560-510}{\sqrt{3600}})$

= P(-1 < z < 1)

= 68%

So Number of scores fall within this interval = 500*0.68 = 340

P(390 < X < 630)

$= P(\frac{390-510}{\sqrt{3600}} < z < \frac{630-510}{\sqrt{3600}})$

= P(-2 < z < 2)

= 95%

So Number of scores fall within this interval = 500*0.95 = 475