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A. A population has a mean of 6.9 and standard deviation of 2.6. Find the value that has 80% of the population below it. (in other words, the 80th percentile).B. A population has mean of 53 and a standard deviation of 34. Find the value that has 35% of the population above it.

Question

A. A population has a mean of 6.9 and standard deviation of 2.6. Find the value that has 80% of the population below it. (in other words, the 80th percentile).

B. A population has mean of 53 and a standard deviation of 34. Find the value that has 35% of the population above it. 

check_circleAnswer
Step 1

Given Population mean = 6.9
Standard deviation = 2.6
The Z score with the area left to it close to 0.80 (0.7995) is 0.84.

0.80
0.0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000
0.5040
0.5080
0.5120
0.5160
0.5199
0.5239
0.5279 0.5319
0.5359
0.5398
0.5753
0.1
0.5438
0.5478
0.5517
0.5557
0.5596
0.5636
0.5675
0.5714
0.5948
0.6026
0.2
0.5793
0.5832
0.5871
0.5910
0.5987
0.6064
0.6103
0.6141
0.6406
0.6443
0.6480
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.6368
0.6517
0.6736
0.4
0.6554
0.6591
0.6628
0.6664
0.6700
0.6772
0.6808
0.6844
0.6879
0.7123
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7157
0.7190
0.7224
0.6
0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.7517
0.7549
0.7734
0.7
0.7580
0.7611
0.7642
0.7673
0.7704
0.7764
0.7794
0.7823
0.7852
0.7995
0.8
0.7881
0.7910
0.7939
0.7967
0.8023
0.8051
0.8078
0.8106
0.8133
0.8159
0.9
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8389
help_outline

Image Transcriptionclose

0.80 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.5398 0.5753 0.1 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5948 0.6026 0.2 0.5793 0.5832 0.5871 0.5910 0.5987 0.6064 0.6103 0.6141 0.6406 0.6443 0.6480 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6517 0.6736 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6772 0.6808 0.6844 0.6879 0.7123 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7734 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7764 0.7794 0.7823 0.7852 0.7995 0.8 0.7881 0.7910 0.7939 0.7967 0.8023 0.8051 0.8078 0.8106 0.8133 0.8159 0.9 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

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Step 2

We use the below formula fo Z score and calculate the 80th percentile value as shown below

The 80th percentile value wth given mean and standard deviation is 9.084

Z=X-
σ
0.84 6.9
2.6
X -6.9 2.184
X 9.084
help_outline

Image Transcriptionclose

Z=X- σ 0.84 6.9 2.6 X -6.9 2.184 X 9.084

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Step 3

Population have mean = 53
Standard deviatoin = 34
The value with 35% of population above it will have 65% of population below it. With reference to the Z table the Z score will be between 0....

0.0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.5279
0.5319
0.0
0.5000
0.5040
0.5080
0.5120
0.5160
0.5199 0.5239
0.5359
0.5517
0.5557
0.5753
0.1
0.5398
0.5438
0.5478
0.5596 0.5636
0.5675
0.5714
0.6064
0.2
0.5793
0.5832
0.5871
0.5910
0.5948
0.5987
0.6026
0.6103
0.6141
0.6443 0.6480
0.6517
0.6217
0.6331
0.3
0.6179
0.6255
0.6293
0.6368 0.6406
0.6664 0.6700
0.6554
0.6591
0.6628
0.6772
0.6808
0.6844
0.6879
0.4
0.6736
0.7157
0.7190
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088 0.7123
0.7224
0.7422
0.7257
0.7324
0.7389
0.7454
0.7517
0.6
0.7291
0.7357
0.7486
0.7549
0.7580
0.7642
0.7
0.7611
0.7673
0.7704
0.7734 0.7764
0.7794
0.7823
0.7852
0.7910
0.7995
0.8051
0.8
0.7881
0.7939
0.7967
0.8023
0.8078
0.8106
0.8133
0.8186
0.9
0.8159
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8389
help_outline

Image Transcriptionclose

0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.5279 0.5319 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5359 0.5517 0.5557 0.5753 0.1 0.5398 0.5438 0.5478 0.5596 0.5636 0.5675 0.5714 0.6064 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6103 0.6141 0.6443 0.6480 0.6517 0.6217 0.6331 0.3 0.6179 0.6255 0.6293 0.6368 0.6406 0.6664 0.6700 0.6554 0.6591 0.6628 0.6772 0.6808 0.6844 0.6879 0.4 0.6736 0.7157 0.7190 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7224 0.7422 0.7257 0.7324 0.7389 0.7454 0.7517 0.6 0.7291 0.7357 0.7486 0.7549 0.7580 0.7642 0.7 0.7611 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7910 0.7995 0.8051 0.8 0.7881 0.7939 0.7967 0.8023 0.8078 0.8106 0.8133 0.8186 0.9 0.8159 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

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