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The number of students reporting readings more than 84 g is (Round to the nearest whole number as needed.) ...

The number of students reporting readings more than 84 g is (Round to the nearest whole number as needed.) ...

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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Suppose 120 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the balance, not all the readings are equal. The results are found to closely approximate a normal curve, with mean 84 g and standard deviation 1 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings more than 84 g. 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 number of students reporting readings more than 84 g is (Round to the nearest whole number as needed.)
Transcribed Image Text:Suppose 120 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the balance, not all the readings are equal. The results are found to closely approximate a normal curve, with mean 84 g and standard deviation 1 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings more than 84 g. 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 number of students reporting readings more than 84 g is (Round to the nearest whole number as needed.)
Standard Normal Curve Areas (page 1) Areas under the Normal Curve s 0 2 z Z A Z A Z A A 0.30 0.60 0.226 0.90 0.316 0.118 0.31 0.122 0.61 0.319 0.229 0.91 0.232 0.92 0.321 1.22 0.236 0.93 0.239 0.94 0.242 0.95 0.00 0.000 0.01 0.004 0.02 0.008 0.32 0.126 0.62 0.03 0.012 0.33 0.129 0.63 0.04 0.016 0.34 0.133 0.64 0.05 0.020 0.35 0.137 0.65 0.06 0.024 0.36 0.141 0.66 0.245 0.96 0.07 0.028 0.37 0.144 0.67 0.249 0.97 0.08 0.032 0.38 0.148 0.68 0.252 0.98 0.09 0.036 0.39 0.152 0.69 0.255 0.99 0.10 0.040 0.40 0.155 0.70 0.258 1.00 0.11 0.044 0.41 0.159 0.71 0.261 1.01 0.12 0.048 0.42 0.163 0.72 0.264 1.02 0.13 0.052 0.43 0.166 0.73 0.267 1.03 0.348 1.33 0.408 1.63 0.14 0.056 0.44 0.170 0.74 0.270 1.04 0.351 1.34 0.410 1.64 0.15 0.060 0.45 0.174 0.75 0.273 1.05 0.353 1.35 0.411 1.65 0.16 0.064 0.46 0.177 0.76 0.276 1.06 0.355 1.36 0.17 0.067 0.47 0.181 0.77 1.07 0.358 1.37 0.18 0.071 0.48 0.184 0.78 0.19 0.075 0.49 0.188 0.79 0.20 0.079 0.50 0.191 0.80 0.21 0.083 0.51 0.195 0.81 0.341 1.30 0.403 1.60 0.344 1.31 0.405 0.346 1.32 0.407 1.62 0.413 1.66 0.279 0.415 1.67 0.282 0.416 1.68 1.08 0.360 1.38 0.285 1.09 0.362 1.39 0.418 1.69 0.288 1.10 0.364 1.40 0.419 1.70 0.291 1.11 0.367 1.41 0.421 1.71 Standard Normal Curve Areas (page 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. The column under A gives the propottion of the area under the entire curve that is between z = 0 and a positive value of z. A 0.464 0.465 0.466 1.98 1.99 2.00 Z 1.80 1.81 1.82 1.83 0.466 2.13 1.84 0.467 2.14 1.85 0.468 2.15 0.484 1.86 0.469 2.16 0.485 1.87 0.469 2.17 1.88 2.18 1.89 Z 2.10 2.11 2.12 2.01 0.470 0.471 2.19 1.90 0.471 2.20 1.91 0.472 2.21 1.92 0.473 2.22 1.93 0.473 2.23 2.24 0.474 1.94 1.95 0.474 2.25 1.96 1.97 0.475 0.476 0.476 2.28 0.477 2.29 0.477 2.30 0.478 2.31 2.46 0.485 2.47 0.493 0.485 2.48 0.493 0.486 2.49 0.486 2.50 0.486 0.487 0.487 2.53 0.487 2.54 0.488 2.55 2.26 0.488 2.56 0.495 2.27 0.488 2.57 0.495 0.489 2.58 0.495 0.489 2.59 0.495 0.489 2.60 0.495 2.61 0.490 0.495 Areas under the Normal Curve 2.42 0.483 2.43 0.484 2.44 2.45 0.494 0.494 0.324 0.326 0.494 2.51 0.494 2.52 0.329 0.331 0.334 0 Z A Z A A 0.482 2.40 0.492 2.70 0.497 0.483 2.41 0.492 2.71 0.483 0.492 2.72 0.497 3.02 0.497 2.73 0.497 3.03 0.492 0.493 2.74 0.497 0.493 2.75 0.497 0.493 2.76 0.497 2.82 0.494 2.83 0.494 2.84 0.495 2.85 2.86 2.87 2.88 2.89 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 1.20 1.21 1.27 0.336 1.28 0.339 1.29 A Z 0.385 1.50 0.387 0.389 1.23 0.391 1.24 0.393 1.25 0.394 1.26 0.498 2.90 0.498 2.91 0.498 A 0.433 0.434 0.436 1.53 0.437 1.54 0.438 1.55 0.396 1.56 1.51 1.52 0.398 1.57 0.400 1.58 0.401 1.59 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. 0.442 0.443 0.444 0.445 1.61 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 Z Z A 3.00 3.30 0.499 3.01 0.499 3.31 0.499 3.32 0.499 0.499 3.04 3.05 0.499 3.06 0.499 2.77 0.497 0.499 3.07 3.37 2.78 0.497 3.08 0.499 3.38 2.79 0.497 3.09 0.499 3.39 2.80 0.497 3.10 0.499 3.40 0.498 2.81 0.499 3.11 3.41 0.499 3.42 3.12 0.498 0.498 3.13 0.499 3.43 0.499 3.44 3.14 0.498 3.15 0.498 3.45 0.498 3.46 0.500 0.498 3.47 3.48 0.499 0.500 0.500 3.49 0.500 0.499 0.499 3.50 0.500 0.499 3.51 0.500 3.18 0.498 3.19 3.20 3.21 0.499 3.16 0.499 3.17 0.499 0.439 0.441 A 0.500 0.500 0.500 3.33 0.500 3.34 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 3.35 3.36
Transcribed Image Text:Standard Normal Curve Areas (page 1) Areas under the Normal Curve s 0 2 z Z A Z A Z A A 0.30 0.60 0.226 0.90 0.316 0.118 0.31 0.122 0.61 0.319 0.229 0.91 0.232 0.92 0.321 1.22 0.236 0.93 0.239 0.94 0.242 0.95 0.00 0.000 0.01 0.004 0.02 0.008 0.32 0.126 0.62 0.03 0.012 0.33 0.129 0.63 0.04 0.016 0.34 0.133 0.64 0.05 0.020 0.35 0.137 0.65 0.06 0.024 0.36 0.141 0.66 0.245 0.96 0.07 0.028 0.37 0.144 0.67 0.249 0.97 0.08 0.032 0.38 0.148 0.68 0.252 0.98 0.09 0.036 0.39 0.152 0.69 0.255 0.99 0.10 0.040 0.40 0.155 0.70 0.258 1.00 0.11 0.044 0.41 0.159 0.71 0.261 1.01 0.12 0.048 0.42 0.163 0.72 0.264 1.02 0.13 0.052 0.43 0.166 0.73 0.267 1.03 0.348 1.33 0.408 1.63 0.14 0.056 0.44 0.170 0.74 0.270 1.04 0.351 1.34 0.410 1.64 0.15 0.060 0.45 0.174 0.75 0.273 1.05 0.353 1.35 0.411 1.65 0.16 0.064 0.46 0.177 0.76 0.276 1.06 0.355 1.36 0.17 0.067 0.47 0.181 0.77 1.07 0.358 1.37 0.18 0.071 0.48 0.184 0.78 0.19 0.075 0.49 0.188 0.79 0.20 0.079 0.50 0.191 0.80 0.21 0.083 0.51 0.195 0.81 0.341 1.30 0.403 1.60 0.344 1.31 0.405 0.346 1.32 0.407 1.62 0.413 1.66 0.279 0.415 1.67 0.282 0.416 1.68 1.08 0.360 1.38 0.285 1.09 0.362 1.39 0.418 1.69 0.288 1.10 0.364 1.40 0.419 1.70 0.291 1.11 0.367 1.41 0.421 1.71 Standard Normal Curve Areas (page 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. The column under A gives the propottion of the area under the entire curve that is between z = 0 and a positive value of z. A 0.464 0.465 0.466 1.98 1.99 2.00 Z 1.80 1.81 1.82 1.83 0.466 2.13 1.84 0.467 2.14 1.85 0.468 2.15 0.484 1.86 0.469 2.16 0.485 1.87 0.469 2.17 1.88 2.18 1.89 Z 2.10 2.11 2.12 2.01 0.470 0.471 2.19 1.90 0.471 2.20 1.91 0.472 2.21 1.92 0.473 2.22 1.93 0.473 2.23 2.24 0.474 1.94 1.95 0.474 2.25 1.96 1.97 0.475 0.476 0.476 2.28 0.477 2.29 0.477 2.30 0.478 2.31 2.46 0.485 2.47 0.493 0.485 2.48 0.493 0.486 2.49 0.486 2.50 0.486 0.487 0.487 2.53 0.487 2.54 0.488 2.55 2.26 0.488 2.56 0.495 2.27 0.488 2.57 0.495 0.489 2.58 0.495 0.489 2.59 0.495 0.489 2.60 0.495 2.61 0.490 0.495 Areas under the Normal Curve 2.42 0.483 2.43 0.484 2.44 2.45 0.494 0.494 0.324 0.326 0.494 2.51 0.494 2.52 0.329 0.331 0.334 0 Z A Z A A 0.482 2.40 0.492 2.70 0.497 0.483 2.41 0.492 2.71 0.483 0.492 2.72 0.497 3.02 0.497 2.73 0.497 3.03 0.492 0.493 2.74 0.497 0.493 2.75 0.497 0.493 2.76 0.497 2.82 0.494 2.83 0.494 2.84 0.495 2.85 2.86 2.87 2.88 2.89 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 1.20 1.21 1.27 0.336 1.28 0.339 1.29 A Z 0.385 1.50 0.387 0.389 1.23 0.391 1.24 0.393 1.25 0.394 1.26 0.498 2.90 0.498 2.91 0.498 A 0.433 0.434 0.436 1.53 0.437 1.54 0.438 1.55 0.396 1.56 1.51 1.52 0.398 1.57 0.400 1.58 0.401 1.59 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. 0.442 0.443 0.444 0.445 1.61 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 Z Z A 3.00 3.30 0.499 3.01 0.499 3.31 0.499 3.32 0.499 0.499 3.04 3.05 0.499 3.06 0.499 2.77 0.497 0.499 3.07 3.37 2.78 0.497 3.08 0.499 3.38 2.79 0.497 3.09 0.499 3.39 2.80 0.497 3.10 0.499 3.40 0.498 2.81 0.499 3.11 3.41 0.499 3.42 3.12 0.498 0.498 3.13 0.499 3.43 0.499 3.44 3.14 0.498 3.15 0.498 3.45 0.498 3.46 0.500 0.498 3.47 3.48 0.499 0.500 0.500 3.49 0.500 0.499 0.499 3.50 0.500 0.499 3.51 0.500 3.18 0.498 3.19 3.20 3.21 0.499 3.16 0.499 3.17 0.499 0.439 0.441 A 0.500 0.500 0.500 3.33 0.500 3.34 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 3.35 3.36
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