The average SAT test scores on both verbal and math components have been compute

Question

The average SAT test scores on both verbal and math components have been computed for students in 50 states and the District of Columbia. Also the proportion of high school graduates taking the test is indicated below:

a) Based on the empirical data, what is the probability of scoring above 550 in math?

b) Using normal distribution theory, what is the probability of scoring above a 550 in math?

State Verbal Math Alabama 561 555 Alaska 520 517 Arizona 523 522 Arkansas 600 340 California 496 514 Colorado 536 539 Connecticut 509 507 Delaware 505 498 Dist. of Columbia 490 475 Florida 499 499 Georgia 486 481 Hawaii 483 512 Idaho 512 438 Illinois 562 578 Indiana 494 497 Iowa 589 601 Kansas 578 575 Kentucky 548 546 Louisiana 560 553 Maine 507 504 Maryland 476 588 Massachusetts 508 508 Michigan 557 566 Minnesota 582 592 Mississippi 567 551 Missouri 567 568 Montana 545 548 Nebraska 562 564 Nevada 508 509 New Hampshire 521 518 New Jersey 589 578 New Mexico 554 545 New York 495 502 North Carolina 490 488 North Dakota 588 595 Ohio 535 536 Oklahoma 460 535 Oregon 525 524 Pennsylvania 498 495 Rhode Island 499 493 South Carolina 479 474 South Dakota 574 570 Tennessee 564 556 Texas 494 501 Utah 576 570 Vermont 508 502 Virginia 506 497 Washington 499 502 West Virginia 524 508 Wisconsin 576 590 Wyoming 543 543

Explanation / Answer

a. Based on empirical data, 17 states has more than 550 in maths out of 50 states.

So, Prob. = 17/50 = 0.34

b. Mean of the math data = 526.8

std. dev of the math data = 45.4

P( marks > 550) = 0.305

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