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The fraction of the population that will receive adequate amounts of vitamins under the given plan is

The fraction of the population that will receive adequate amounts of vitamins under the given plan is

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.6 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. ... The fraction of the population that will receive adequate amounts of vitamins under the given plan is as needed.) (Type an integer or decimal rounded to the nearest thousandth
Transcribed Image Text:In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.6 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. ... The fraction of the population that will receive adequate amounts of vitamins under the given plan is as needed.) (Type an integer or decimal rounded to the nearest thousandth
Standard Normal Curve Areas (page 1) Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z = 0 and a positive value of z. 0 A Z A Z Z A z A 0.316 1.20 0.385 0.319 1.21 0.387 1.22 1.23 0.391 1.53 0.389 1.52 Z A 0.00 0.000 0.30 0.118 0.60 0.226 0.90 0.01 0.004 0.31 0.122 0.61 0.229 0.91 0.02 0.008 0.32 0.126 0.62 0.232 0.92 0.03 0.012 0.33 0.129 0.63 0.236 0.93 0.04 0.016 0.34 0.133 0.64 0.239 0.94 0.05 0.020 0.35 0.137 0.242 0.95 0.06 0.024 0.36 0.07 0.028 0.37 0.08 0.032 0.38 0.09 0.036 0.39 0.10 0.040 0.40 0.155 0.65 0.141 0.66 0.245 0.96 0.321 0.324 0.326 1.24 0.393 1.54 0.329 1.25 0.394 1.55 0.331 1.26 0.396 1.56 0.249 0.97 0.334 1.27 0.398 1.57 0.148 0.68 0.252 0.98 0.336 1.28 0.152 0.69 0.255 0.99 0.339 1.29 0.70 0.258 1.00 0.341 1.30 0.71 1.01 0.344 1.31 0.144 0.67 0.400 1.58 0.401 1.59 0.403 1.60 0.11 0.044 0.41 0.159 0.261 0.405 1.61 0.12 0.048 0.42 0.163 0.72 0.264 0.346 1.32 0.407 1.62 0.13 0.052 0.43 0.166 0.73 0.267 1.02 1.03 1.04 0.351 0.408 1.63 0.14 0.056 0.44 0.170 0.74 1.34 0.410 1.64 1.35 0.411 1.65 1.66 0.270 0.15 0.060 0.45 0.174 0.75 0.273 1.05 0.353 0.16 0.064 0.46 0.177 0.76 0.276 1.06 0.17 0.067 0.47 0.181 0.77 0.279 1.07 0.358 0.18 0.071 0.48 0.184 0.78 0.282 1.08 0.360 0.19 0.075 0.49 0.188 0.79 0.285 1.09 0.362 0.80 1.10 0.364 1.67 0.355 1.36 0.413 1.37 0.415 1.38 0.416 1.68 1.69 0.20 0.079 0.50 0.191 0.288 0.419 1.70 0.21 0.083 0.51 0.195 0.81 0.291 1.11 0.367 1.39 0.418 1.40 1.41 0.421 1.42 1.43 0.424 1.73 1.71 0.22 0.087 0.52 0.198 0.82 0.294 1.12 0.369 0.422 1.72 0.23 0.091 0.53 0.202 0.83 0.297 1.13 0.371 0.24 0.095 0.54 0.205 0.84 0.300 1.14 0.373 1.44 0.425 1.74 0.302 1.15 0.375 1.45 0.426 1.75 0.099 0.55 0.103 0.56 0.25 0.209 0.85 0.26 0.212 0.86 0.305 1.16 0.377 1.46 0.428 1.76 0.27 0.106 0.57 0.216 0.87 0.308 1.17 0.379 1.47 0.429 1.77 0.28 0.110 0.58 0.219 0.88 0.311 1.18 0.381 1.48 0.431 1.78 Standard Normal Curve Areas (page 2) Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. 2 The column under A gives the proportion of the area under the entire curve that is between z = 0 and a positive value of z. 0.348 1.33 Areas under the Normal Curve A 0 z 1.50 1.51 A 0.433 0.434 0.436 0.437 0.438 0.439 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 0.457 0.458 0.459 0.460 0.461 0.462 0.462 Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. z A Z A Z Z A 0.497 Z A Z 3.00 0.499 3.30 0.497 3.01 0.499 3.31 0.499 3.32 0.500 0.499 3.33 0.500 0.500 0.500 A 1.80 0.464 2.10 0.482 2.40 0.492 2.70 1.81 0.465 2.11 0.483 2.41 0.492 2.71 1.82 0.466 2.12 0.483 2.42 0.492 2.72 0.497 3.02 1.83 0.466 2.13 0.483 2.43 0.492 2.73 0.497 3.03 1.84 0.467 2.14 0.484 2.44 0.493 2.74 0.497 3.04 0.499 3.34 1.85 0.468 2.15 0.484 2.45 0.493 2.75 0.497 3.05 0.499 3.35 1.86 0.469 2.16 0.485 2.46 0.493 2.76 0.497 3.06 0.499 3.36 0.485 2.47 0.493 2.77 1.88 0.470 2.18 0.485 2.48 0.493 2.78 0.497 1.89 0.471 2.19 0.486 2.49 0.494 1.90 0.471 2.20 0.486 2.50 0.494 0.494 0.494 0.500 1.87 0.469 2.17 0.497 3.07 0.499 3.37 0.500 3.08 0.499 3.38 0.500 2.79 0.497 3.09 0.499 3.39 0.500 0.499 3.40 0.500 1.91 0.472 2.21 0.486 2.51 0.499 3.41 0.500 2.80 0.497 3.10 2.81 0.498 3.11 2.82 0.498 3.12 0.499 3.42 0.500 2.83 0.498 3.13 0.499 0.498 3.14 0.499 0.494 3.43 0.500 3.44 0.500 3.45 0.500 2.84 2.85 0.498 3.15 0.499 0.498 3.16 0.498 3.17 0.499 3.46 0.499 3.47 1.92 0.473 2.22 0.487 2.52 1.93 0.473 2.23 0.487 2.53 1.94 0.474 2.24 0.487 2.54 0.494 1.95 0,474 2.25 0.488 2.55 0.495 1.96 0.475 2.26 0.488 2.56 0.495 2.86 1.97 0.476 2.27 0.488 2.57 0.495 2.87 1.98 0.476 2.28 0.489 2.58 0.495 2.88 0.498 3.18 1.99 0.477 2.29 0.489 2.59 0.495 2.89 0.498 3.19 2.00 0.477 2.30 0.489 2.60 0.495 2.90 0.498 3.20 2.01 0.478 2.31 0.490 2.61 0.495 2.91 0.498 3.21 2.02 0.478 2.32 0.490 2.62 0.496 2.92 2.03 0.479 2.33 0.490 2.63 0.496 2.93 2.04 0.479 2.34 0.490 2.64 0.496 2.94 2.05 0.480 2.35 0.491 2.65 0.496 2.95 2.06 0.480 2.36 0.491 2.66 0.496 2.96 2.07 0.481 2.37 0.491 2.67 0.496 2.97 0.499 2.08 0.481 2.38 0.491 2.68 0.496 2.98 0.499 2.09 0.482 2.39 0.492 2.69 0.496 2.99 0.498 3.22 0.498 3.23 0.498 3.24 0.498 0.498 0.499 A 0.500 0.500 0.500 0.500 0.499 3.48 0.500 0.499 3.49 0.500 0.499 3.50 0.500 0.499 3.51 0.500 0.500 0.500 3.27 0.499 3.57 3.28 0.499 3.58 3.29 0.499 3.59 0.499 3.52 0.499 3.53 0.499 3.54 0.500 3.25 0.499 3.55 0.500 3.26 0.499 3.56 0.500 0.500 0.500 0.500
Transcribed Image Text:Standard Normal Curve Areas (page 1) Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z = 0 and a positive value of z. 0 A Z A Z Z A z A 0.316 1.20 0.385 0.319 1.21 0.387 1.22 1.23 0.391 1.53 0.389 1.52 Z A 0.00 0.000 0.30 0.118 0.60 0.226 0.90 0.01 0.004 0.31 0.122 0.61 0.229 0.91 0.02 0.008 0.32 0.126 0.62 0.232 0.92 0.03 0.012 0.33 0.129 0.63 0.236 0.93 0.04 0.016 0.34 0.133 0.64 0.239 0.94 0.05 0.020 0.35 0.137 0.242 0.95 0.06 0.024 0.36 0.07 0.028 0.37 0.08 0.032 0.38 0.09 0.036 0.39 0.10 0.040 0.40 0.155 0.65 0.141 0.66 0.245 0.96 0.321 0.324 0.326 1.24 0.393 1.54 0.329 1.25 0.394 1.55 0.331 1.26 0.396 1.56 0.249 0.97 0.334 1.27 0.398 1.57 0.148 0.68 0.252 0.98 0.336 1.28 0.152 0.69 0.255 0.99 0.339 1.29 0.70 0.258 1.00 0.341 1.30 0.71 1.01 0.344 1.31 0.144 0.67 0.400 1.58 0.401 1.59 0.403 1.60 0.11 0.044 0.41 0.159 0.261 0.405 1.61 0.12 0.048 0.42 0.163 0.72 0.264 0.346 1.32 0.407 1.62 0.13 0.052 0.43 0.166 0.73 0.267 1.02 1.03 1.04 0.351 0.408 1.63 0.14 0.056 0.44 0.170 0.74 1.34 0.410 1.64 1.35 0.411 1.65 1.66 0.270 0.15 0.060 0.45 0.174 0.75 0.273 1.05 0.353 0.16 0.064 0.46 0.177 0.76 0.276 1.06 0.17 0.067 0.47 0.181 0.77 0.279 1.07 0.358 0.18 0.071 0.48 0.184 0.78 0.282 1.08 0.360 0.19 0.075 0.49 0.188 0.79 0.285 1.09 0.362 0.80 1.10 0.364 1.67 0.355 1.36 0.413 1.37 0.415 1.38 0.416 1.68 1.69 0.20 0.079 0.50 0.191 0.288 0.419 1.70 0.21 0.083 0.51 0.195 0.81 0.291 1.11 0.367 1.39 0.418 1.40 1.41 0.421 1.42 1.43 0.424 1.73 1.71 0.22 0.087 0.52 0.198 0.82 0.294 1.12 0.369 0.422 1.72 0.23 0.091 0.53 0.202 0.83 0.297 1.13 0.371 0.24 0.095 0.54 0.205 0.84 0.300 1.14 0.373 1.44 0.425 1.74 0.302 1.15 0.375 1.45 0.426 1.75 0.099 0.55 0.103 0.56 0.25 0.209 0.85 0.26 0.212 0.86 0.305 1.16 0.377 1.46 0.428 1.76 0.27 0.106 0.57 0.216 0.87 0.308 1.17 0.379 1.47 0.429 1.77 0.28 0.110 0.58 0.219 0.88 0.311 1.18 0.381 1.48 0.431 1.78 Standard Normal Curve Areas (page 2) Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. 2 The column under A gives the proportion of the area under the entire curve that is between z = 0 and a positive value of z. 0.348 1.33 Areas under the Normal Curve A 0 z 1.50 1.51 A 0.433 0.434 0.436 0.437 0.438 0.439 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 0.457 0.458 0.459 0.460 0.461 0.462 0.462 Because the curve is symmetric about 0, the area between z = 0 and a negative value of z can be found by using the corresponding positive value of z. z A Z A Z Z A 0.497 Z A Z 3.00 0.499 3.30 0.497 3.01 0.499 3.31 0.499 3.32 0.500 0.499 3.33 0.500 0.500 0.500 A 1.80 0.464 2.10 0.482 2.40 0.492 2.70 1.81 0.465 2.11 0.483 2.41 0.492 2.71 1.82 0.466 2.12 0.483 2.42 0.492 2.72 0.497 3.02 1.83 0.466 2.13 0.483 2.43 0.492 2.73 0.497 3.03 1.84 0.467 2.14 0.484 2.44 0.493 2.74 0.497 3.04 0.499 3.34 1.85 0.468 2.15 0.484 2.45 0.493 2.75 0.497 3.05 0.499 3.35 1.86 0.469 2.16 0.485 2.46 0.493 2.76 0.497 3.06 0.499 3.36 0.485 2.47 0.493 2.77 1.88 0.470 2.18 0.485 2.48 0.493 2.78 0.497 1.89 0.471 2.19 0.486 2.49 0.494 1.90 0.471 2.20 0.486 2.50 0.494 0.494 0.494 0.500 1.87 0.469 2.17 0.497 3.07 0.499 3.37 0.500 3.08 0.499 3.38 0.500 2.79 0.497 3.09 0.499 3.39 0.500 0.499 3.40 0.500 1.91 0.472 2.21 0.486 2.51 0.499 3.41 0.500 2.80 0.497 3.10 2.81 0.498 3.11 2.82 0.498 3.12 0.499 3.42 0.500 2.83 0.498 3.13 0.499 0.498 3.14 0.499 0.494 3.43 0.500 3.44 0.500 3.45 0.500 2.84 2.85 0.498 3.15 0.499 0.498 3.16 0.498 3.17 0.499 3.46 0.499 3.47 1.92 0.473 2.22 0.487 2.52 1.93 0.473 2.23 0.487 2.53 1.94 0.474 2.24 0.487 2.54 0.494 1.95 0,474 2.25 0.488 2.55 0.495 1.96 0.475 2.26 0.488 2.56 0.495 2.86 1.97 0.476 2.27 0.488 2.57 0.495 2.87 1.98 0.476 2.28 0.489 2.58 0.495 2.88 0.498 3.18 1.99 0.477 2.29 0.489 2.59 0.495 2.89 0.498 3.19 2.00 0.477 2.30 0.489 2.60 0.495 2.90 0.498 3.20 2.01 0.478 2.31 0.490 2.61 0.495 2.91 0.498 3.21 2.02 0.478 2.32 0.490 2.62 0.496 2.92 2.03 0.479 2.33 0.490 2.63 0.496 2.93 2.04 0.479 2.34 0.490 2.64 0.496 2.94 2.05 0.480 2.35 0.491 2.65 0.496 2.95 2.06 0.480 2.36 0.491 2.66 0.496 2.96 2.07 0.481 2.37 0.491 2.67 0.496 2.97 0.499 2.08 0.481 2.38 0.491 2.68 0.496 2.98 0.499 2.09 0.482 2.39 0.492 2.69 0.496 2.99 0.498 3.22 0.498 3.23 0.498 3.24 0.498 0.498 0.499 A 0.500 0.500 0.500 0.500 0.499 3.48 0.500 0.499 3.49 0.500 0.499 3.50 0.500 0.499 3.51 0.500 0.500 0.500 3.27 0.499 3.57 3.28 0.499 3.58 3.29 0.499 3.59 0.499 3.52 0.499 3.53 0.499 3.54 0.500 3.25 0.499 3.55 0.500 3.26 0.499 3.56 0.500 0.500 0.500 0.500
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