You run a gizmo factory. The following data shows the daily output of your factory for the past year. 488 462 492 480 470 495 467 476 494 474 496 500 495 499 494 481 477 481 468 470 476 479 478 471 484 492 477 488 489 488 499 491 486 477 503 484 532 515 476 493 475 484 498 476 483 506 467 444 466 464 478 454 473 465 491 460 470 483 446 471 529 493 471 468 505 467 506 501 492 477 478 486 454 492 500 471 467 477 485 472 475 493 447 508 478 446 500 496 494 485 493 477 511 487 498 512 446 489 458 461 461 486 501 484 470 477 484 464 491 470 478 480 491 462 483 476 476 483 490 457 511 517 478 499 479 467 500 484 487 473 472 481 458 471 495 451 485 491 482 470 507 498 491 433 488 501 496 446 482 477 467 462 473 466 503 461 511 524 459 487 474 468 485 497 457 448 460 493 494 463 480 475 479 506 485 460 494 480 480 463 510 490 477 470 494 483 474 466 471 475 487 502 502 482 442 468 490 511 499 487 472 458 469 463 498 470 501 486 461 499 497 493 445 477 456 451 461 485 492 472 493 515 489 487 485 509 502 484 461 486 490 462 481 484 463 480 465 508 490 480 450 503 496 491 479 485 469 449 479 458 489 466 477 479 496 481 499 475 480 486 414 454 452 492 504 482 451 450 445 485 465 487 492 449 496 480 465 482 506 494 480 480 490 501 477 520 502 472 473 466 476 469 475 493 467 464 505 455 499 490 469 470 485 492 445 473 465 489 511 462 502 483 510 481 471 433 477 497 500 474 437 467 496 470 470 469 466 483 472 457 467 473 491 472 471 461 496 452 503 463 461 475 479 451 469 468 481 485 473 457 499 464 483 471 451 466 478 499 462 476 You take repeated random samples of size n = 25 days from the above population data.     1 The expected value of the sample means is _______.           a 484.472                   b 479.675                   c 474.926                   d 470.224                                         2 In the previous question the variance of the sample mean is.         a 9.781                   b 12.226                   c 61.132                   d 305.658                                         3 Using the population mean and standard deviation in question 1, what is the probability that the mean of a random sample of n = 25 days exceeds 485 gizmos?   a 0.0639                   b 0.0799                   c 0.0998                   d 0.1248

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.