Question

3-2

Almost all companies utilize some type of? year-end performance review for their employees. Human Resources? (HR) at a? university's Health Science Center provides guidelines for supervisors rating their subordinates. For? example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to? HR, "if you have this? tendency, consider using a normal distribution —?10% of employees? (rated) exemplary,? 20% distinguished,? 40% competent,? 20% marginal, and? 10% unacceptable." Suppose you are rating an? employee's performance on a scale of 1? (lowest) to 100? (highest). Also, assume the ratings follow a normal distribution with a mean of 49 and a standard deviation of 15.

Complete parts a and b.

View a table of areas under the standardized normal curve.

z           .00        .01        .02        .03        .04        .05        .06        .07        .08        .09

.0         .0000    .0040    .0080    .0120    .0160    .0199    .0239    .0279    .0319    .0359

.1         .0398    .0438    .0478    .0517    .0557    .0596    .0636    .0675    .0714    .0753

.2         .0793    .0832    .0871    .0910    .0948    .0987    .1026    .1064    .1103    .1141

.3         .1179    .1217    .1255    .1293    .1331    .1368    .1406    .1443    .1480    .1517

.4         .1554    .1591    .1628    .1664    .1700    .1736    .1772    .1808    .1844    .1879

.5         .1915    .1950    .1985    .2019    .2054    .2088    .2123    .2157    .2190    .2224

.6         .2257    .2291    .2324    .2357    .2389    .2422    .2454    .2486    .2517    .2549

.7         .2580    .2611    .2642    .2673    .2704    .2734    .2764    .2794    .2823    .2852

.8         .2881    .2910    .2939    .2967    .2995    .3023    .3051    .3078    .3106    .3133

.9         .3159    .3186    .3212    .3238    .3264    .3289    .3315    .3340    .3365    .3389

1.0        .3413    .3438    .3461    .3485    .3508    .3531    .3554    .3577    .3599    .3621

1.1        .3643    .3665    .3686    .3708    .3729    .3749    .3770    .3790    .3810    .3830

1.2        .3849    .3869    .3888    .3907    .3925    .3944    .3962    .3980    .3997    .4015

1.3        .4032    .4049    .4066    .4082    .4099    .4115    .4131    .4147    .4162    .4177

1.4        .4192    .4207    .4222    .4236    .4251    .4265    .4279    .4292    .4306    .4319

1.5        .4332    .4345    .4357    .4370    .4382    .4394    .4406    .4418    .4429    .4441

1.6        .4452    .4463    .4474    .4484    .4495    .4505    .4515    .4525    .4535    .4545

1.7        .4554    .4564    .4573    .4582    .4591    .4599    .4608    .4616    .4625    .4633

1.8        .4641    .4649    .4656    .4664    .4671    .4678    .4686    .4693    .4699    .4706

1.9        .4713    .4719    .4726    .4732    .4738    .4744    .4750    .4756    .4761    .4767

2.0        .4772    .4778    .4783    .4788    .4793    .4798    .4803    .4808    .4812    .4817

2.1        .4821    .4826    .4830    .4834    .4838    .4842    .4846    .4850    .4854    .4857

2.2        .4861    .4864    .4868    .4871    .4875    .4878    .4881    .4884    .4887    .4890

2.3        .4893    .4896    .4898    .4901    .4904    .4906    .4909    .4911    .4913    .4916

2.4        .4918    .4920    .4922    .4925    .4927    .4929    .4931    .4932    .4934    .4936

2.5        .4938    .4940    .4941    .4943    .4945    .4946    .4948    .4949    .4951    .4952

2.6        .4953    .4955    .4956    .4957    .4959    .4960    .4961    .4962    .4963    .4964

2.7        .4965    .4966    .4967    .4968    .4969    .4970    .4971    .4972    .4973    .4974

2.8        .4974    .4975    .4976    .4977    .4977    .4978    .4979    .4979    .4980    .4981

2.9        .4981    .4982    .4982    .4983    .4984    .4984    .4985    .4985    .4986    .4986

3.0        .4987    .4987    .4987    .4988    .4988    .4989    .4989    .4989    .4990    .4990

3.1        .49903   .49906   .49910   .49913   .49916   .49918   .49921   .49924   .49926   .49929

3.2        .49931   .49934   .49936   .49938   .49940   .49942   .49944   .49946   .49948   .49950

3.3        .49952   .49953   .49955   .49957   .49958   .49960   .49961   .49962   .49964   .49965

3.4        .49966   .49968   .49969   .49970   .49971   .49972   .49973   .49974   .49975   .49976

3.5        .49977   .49978   .49978   .49979   .49980   .49981   .49981   .49982   .49983   .49983

3.6        .49984   .49985   .49985   .49986   .49986   .49987   .49987   .49988   .49988   .49989

3.7        .49989   .49990   .49990   .49990   .49991   .49991   .49992   .49992   .49992   .49992

3.8        .49993   .49993   .49993   .49994   .49994   .49994   .49994   .49995   .49995   .49995

3.9        .49995   .49995   .49996   .49996   .49996   .49996   .49996   .49996   .49997   .49997

a. What is the lowest rating you should give to an? "exemplary" employee if you follow the? university's HR? guidelines? --- ------ (Round to two decimal places as? needed.)

b. What is the lowest rating you should give to a? "competent" employee if you follow the? university's guidelines? ------- (Round to two decimal places as? needed.)

3- 3

Personnel tests are designed to test a job? applicant's cognitive? and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last?year, the distribution of scores was approximately normal with mean 78 and standard deviation 8.4.

a. A particular employer requires job candidates to score at least 82 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 82??

b. The testing service reported to a particular employer that one of its job? candidate's scores fell at the 90th percentile of the distribution? (i.e., approximately 90?% of the scores were lower than the? candidate's, and only 10?% were? higher). What was the? candidate's score?

View a table of areas under the standardized normal curve.

z           0.00      0.01      0.02      0.03      0.04      0.05      0.06      0.07      0.08      0.09

0.0        0.0000   0.0040   0.0080   0.0120   0.0160   0.0199   0.0239   0.0279   0.0319   0.0359

0.1        0.0398   0.0438   0.0478   0.0517   0.0557   0.0596   0.0636   0.0675   0.0714   0.0753

0.2        0.0793   0.0832   0.0871   0.0910   0.0948   0.0987   0.1026   0.1064   0.1103   0.1141

0.3        0.1179   0.1217   0.1255   0.1293   0.1331   0.1368   0.1406   0.1443   0.1480   0.1517

0.4        0.1554   0.1591   0.1628   0.1664   0.1700   0.1736   0.1772   0.1808   0.1844   0.1879

0.5        0.1915   0.1950   0.1985   0.2019   0.2054   0.2088   0.2123   0.2157   0.2190   0.2224

0.6        0.2257   0.2291   0.2324   0.2357   0.2389   0.2422   0.2454   0.2486   0.2517   0.2549

0.7        0.2580   0.2611   0.2642   0.2673   0.2704   0.2734   0.2764   0.2794   0.2823   0.2852

0.8        0.2881   0.2910   0.2939   0.2967   0.2995   0.3023   0.3051   0.3078   0.3106   0.3133

0.9        0.3159   0.3186   0.3212   0.3238   0.3264   0.3289   0.3315   0.3340   0.3365   0.3389

1.0        0.3413   0.3438   0.3461   0.3485   0.3508   0.3531   0.3554   0.3577   0.3599   0.3621

1.1        0.3643   0.3665   0.3686   0.3708   0.3729   0.3749   0.3770   0.3790   0.3810   0.3830

1.2        0.3849   0.3869   0.3888   0.3907   0.3925   0.3944   0.3962   0.3980   0.3997   0.4015

1.3        0.4032   0.4049   0.4066   0.4082   0.4099   0.4115   0.4131   0.4147   0.4162   0.4177

1.4        0.4192   0.4207   0.4222   0.4236   0.4251   0.4265   0.4279   0.4292   0.4306   0.4319

1.5        0.4332   0.4345   0.4357   0.4370   0.4382   0.4394   0.4406   0.4418   0.4429   0.4441

1.6        0.4452   0.4463   0.4474   0.4484   0.4495   0.4505   0.4515   0.4525   0.4535   0.4545

1.7        0.4554   0.4564   0.4573   0.4582   0.4591   0.4599   0.4608   0.4616   0.4625   0.4633

1.8        0.4641   0.4649   0.4656   0.4664   0.4671   0.4678   0.4686   0.4693   0.4699   0.4706

1.9        0.4713   0.4719   0.4726   0.4732   0.4738   0.4744   0.4750   0.4756   0.4761   0.4767

2.0        0.4772   0.4778   0.4783   0.4788   0.4793   0.4798   0.4803   0.4808   0.4812   0.4817

2.1        0.4821   0.4826   0.4830   0.4834   0.4838   0.4842   0.4846   0.4850   0.4854   0.4857

2.2        0.4861   0.4864   0.4868   0.4871   0.4875   0.4878   0.4881   0.4884   0.4887   0.4890

2.3        0.4893   0.4896   0.4898   0.4901   0.4904   0.4906   0.4909   0.4911   0.4913   0.4916

2.4        0.4918   0.4920   0.4922   0.4925   0.4927   0.4929   0.4931   0.4932   0.4934   0.4936

2.5        0.4938   0.4940   0.4941   0.4943   0.4945   0.4946   0.4948   0.4949   0.4951   0.4952

2.6        0.4953   0.4955   0.4956   0.4957   0.4959   0.4960   0.4961   0.4962   0.4963   0.4964

2.7        0.4965   0.4966   0.4967   0.4968   0.4969   0.4970   0.4971   0.4972   0.4973   0.4974

2.8        0.4974   0.4975   0.4976   0.4977   0.4977   0.4978   0.4979   0.4979   0.4980   0.4981

2.9        0.4981   0.4982   0.4982   0.4983   0.4984   0.4984   0.4985   0.4985   0.4986   0.4986

3.0        0.4987   0.4987   0.4987   0.4988   0.4988   0.4989   0.4989   0.4989   0.4990   0.4990

3.1        0.49903 0.49906 0.49910 0.49913 0.49916 0.49918 0.49921 0.49924 0.49926 0.49929

3.2        0.49931 0.49934 0.49936 0.49938 0.49940 0.49942 0.49944 0.49946 0.49948 0.49950

3.3        0.49952 0.49953 0.49955 0.49957 0.49958 0.49960 0.49961 0.49962 0.49964 0.49965

3.4        0.49966 0.49968 0.49969 0.49970 0.49971 0.49972 0.49973 0.49974 0.49975 0.49976

3.5        0.49977 0.49978 0.49978 0.49979 0.49980 0.49981 0.49981 0.49982 0.49983 0.49983

3.6        0.49984 0.49985 0.49985 0.49986 0.49986 0.49987 0.49987 0.49988 0.49988 0.49989

3.7        0.49989 0.49990 0.49990 0.49990 0.49991 0.49991 0.49992 0.49992 0.49992 0.49992

3.8        0.49993 0.49993 0.49993 0.49994 0.49994 0.49994 0.49994 0.49995 0.49995 0.49995

3.9        0.49995 0.49995 0.49996 0.49996 0.49996 0.49996 0.49996 0.49996 0.49997 0.49997

a. Approximately ----?% of the test scores during the past year exceeded 82. ?(Round to one decimal place as? needed.)

b. The? candidate's score was ----. (Round to the nearest whole number as? needed.)

Answer 1

we observe that the employees ratings follows normal distribution with mean rating 49 and standard deviation 15.

a. we know that 10% of the employees are exemplary.

let us suppose that the lowest rating we should give to an exemplary employee is x.

by normal distribution p(X>x)0.10

0.5-p(0<X<x)0.10

p(0<X<x)0.40

from the normal tables the value of p(0<X<x)0.40 is 1.285

if you substitute this value in standard normal variate we will get the value of x=68.275

hence the lowest rating you should give to an exemplary employee is 68.275

b. we know that 40% of the employees comes under competant employees

let us suppose that the lowest rating we should give to a competant employee is y

p(X>y)0.40

0.5+P(0<X<y)0.10

from the normal tables the value of p(0<X<y)0.10 is 0.255

if you substitute this value in the standard normal variate we will get the value of y=52.825

hence the lowest score we should give to a competant employee is 52.825