Question

a) A study was done to assess the awareness of professionals in accounting, teaching and medicine about new developments in science and technology. A sample group of 955 professionals was taken and given a test. Some 410 of the professionals passed the test. Among those who passed the test 155 were accountants. Among the failures, 180 were accountants and 195 teachers. The number of teachers in the study was 345.
Required:
i). Filling in all the blank spaces, present the information in tabular form. [6 marks]
ii). If the study recommends that any professional group with more that 45% failures should enroll for an in-service programme. (Show your workings) [3 marks]
iii). The probability that a professional in accounting, medicine or teaching failed the test. (3 MKS)

Answer 1

Answer to Question #91015 – Math – Statistics and Probability

Question

a) A study was done to assess the awareness of professionals in accounting, teaching and medicine about new developments in science and technology. A sample group of 955 professionals was taken and given a test. Some 410 of the professionals passed the test. Among those who passed the test 155 were accountants. Among the failures, 180 were accountants and 195 teachers. The number of teachers in the study was 345.

Required:

i). Filling in all the blank spaces, present the information in tabular form. [6 marks]

ii). If the study recommends that any professional group with more than 45% failures should enroll for an in-service programme. (Show your workings) [3 marks]

iii). The probability that a professional in accounting, medicine or teaching failed the test. (3 MKS)

Solution

(i)

Given

Total no. of professional=955

Total no. professionals who passed the test=410

Total no. accountants who passed the test=155

The number of teachers in the study =345.

Therefore,

Total no. professionals who Failed the test = Total no. of professional- Total no. professionals who passed the test

Total no. professionals who Failed the test =955-410=545

Total no. accountants who Failed the test=180

Total no. teachers who Failed the test=195

Medicine Professional who Failed the test=(professionals who Failed the test - failed accountant - teachers failed)

Medicine Professional who Failed the test=(545 - 180 - 195)=170

Number of teachers passed = number of teachers in the study - no. of teacher failed

Number of teachers passed=345-195=150

Medicine Professional who Pass the test=(professionals who Pass the test - passed accountant - teachers passed)

Medicine Professional who Pass the test=(410- 150 - 155)=105

(ii) Failure percentage for Teachers $\frac{\text{total teacher who failed the test}}{\text{total no.of teachers}} \times 100$

Failure% for Teachers $\frac{195}{195 + 150} \times 100 = \frac{195}{345} \times 100 = 56.52\%$

Failure percentage for Accountants $\frac{\text{total Accountants who failed the test}}{\text{total no.of Accountants}} \times 100$

Failure% for Accountants $\frac{155}{155 + 180} \times 100 = \frac{155}{335} \times 100 = 46.27\%$

Failure % for Medicine

Professionals $\frac{\text{total Medicine Professionals who failed the test}}{\text{total no.of Medicine Professionals}} \times 100$

Failure% for Medicine Professionals $\frac{170}{170 + 105} \times 100 = \frac{170}{285} \times 100 = 59.65\%$

(iii)

Probability of failure for Teachers= $\frac{\text{total teacher who failed the test}}{\text{total no.of teachers}}$

Probability of failure for Teachers= $\frac{195}{195+150} = \frac{195}{345} = 0.5652$

Probability of failure for Accountants= $\frac{\text{total Accountants who failed the test}}{\text{total no.of Accountants}}$

Probability of failure for Accountants = $\frac{155}{155+180} = \frac{155}{335} \times 100 = 0.46.27$

Probability of failure for Medicine Professionals= $\frac{\text{total Medicine Professionals who failed the test}}{\text{total no.of Medicine Professionals}}$

Probability of failure for Medicine Professionals = $\frac{170}{170+105} = \frac{170}{285} = 0.59.65$

Answer provided by https://www.AssignmentExpert.com