Question

1) Mathematics achievement test scores for 500 students were found to have a mean and a variance equal to 590 and 4900, respectively. If the distribution of test scores was mound-shaped, approximately how many of the scores would fall into the interval 520 to 660? (Round your answer to the nearest whole number.)

2) Approximately how many scores would be expected to fall into the interval 450 to 730? (Round your answer to the nearest whole number.)

Answer 1

Given,

= 590, = sqrt(4900) = 70

We convert this to standard normal as

P(X < x) = P( Z < x - / )

So,

P( 520 < X < 660) = P( X < 660) - P( X < 520)

= P( Z < 660 - 590 / 70) - P( Z < 520 - 590 / 70)

= P( Z < 1) - P( Z < -1)

= P( Z < 1) - ( 1 - P( Z < 1))

= 0.8413 - ( 1 - 0.8413)

= 0.6827

So, In the 500 students, number of scores would fall into the interval 520 to 660 is

= 500 * 0.6827

= 341.35

= 341 (ROunded to nearest whole number)