4. (a) In the claims department of an insurance office various quantities are computed at the end of each day's business. On Monday, 20 claims are received for a particular class of policy. The mean claim amount is calculated to be K4,500 and the standard deviation to be K2,540. On Tuesday, the claims are reviewed and one claim which was incorrectly recorded as K13,000 is now corrected to K3,000. Determine the mean and standard deviation of the corrected set of claims. (b) Last year two groups of students (part-time and distance) sat for the same GBS 541 exam. The marks in the part-time group of 64 students had an average of 52 and a standard deviation of 9. The marks in the distance group of 42 students had an average of 45 and a standard deviation of 8. Calculate the average and standard deviation of the combined set of 106 students.
4. (a) In the claims department of an insurance office various quantities are computed at the end of each day's business. On Monday, 20 claims are received for a particular class of policy. The mean claim amount is calculated to be K4,500 and the standard deviation to be K2,540. On Tuesday, the claims are reviewed and one claim which was incorrectly recorded as K13,000 is now corrected to K3,000. Determine the mean and standard deviation of the corrected set of claims. (b) Last year two groups of students (part-time and distance) sat for the same GBS 541 exam. The marks in the part-time group of 64 students had an average of 52 and a standard deviation of 9. The marks in the distance group of 42 students had an average of 45 and a standard deviation of 8. Calculate the average and standard deviation of the combined set of 106 students.
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Transcribed Image Text:4. (a) In the claims department of an insurance office various quantities are computed at the
end of each day's business. On Monday, 20 claims are received for a particular class of
policy. The mean claim amount is calculated to be K4,500 and the standard deviation
to be K2,540. On Tuesday, the claims are reviewed and one claim which was
incorrectly recorded as K13,000 is now corrected to K3,000.
Determine the mean and standard deviation of the corrected set of claims.
(4)
(b) Last year two groups of students (part-time and distance) sat for the same GBS 541
exam. The marks in the part-time group of 64 students had an average of 52 and a
standard deviation of 9. The marks in the distance group of 42 students had an
average of 45 and a standard deviation of 8.
(4)
Calculate the average and standard deviation of the combined set of 106 students.
5. An insurance company has a portfolio of 10,000 policies. Based on past data the company
estimates that the probability of a claim on any one policy in a year is 0.003. It assumes no
policy will generate more than one claim in a year.
(a) Determine the approximate probability of more than 40 claims from the portfolio
of 10,000 policies in a year.
(4)
(b) Determine an approximate equal-tailed interval into which the number of claims
Transcribed Image Text:(4)
Calculate the average and standard deviation of the combined set of 106 students.
5. An insurance company has a portfolio of 10,000 policies. Based on past data the company
estimates that the probability of a claim on any one policy in a year is 0.003. It assumes no
policy will generate more than one claim in a year.
(a) Determine the approximate probability of more than 40 claims from the portfolio
of 10,000 policies in a year.
(4)
(b) Determine an approximate equal-tailed interval into which the number of claims
Page 3 of 4
per
will fall with
y 0.95.
(2)
(c) In practice 42 claims were received in a particular year. A Director of the company complains
about the range of estimates in part (b) being wrong.
Comment on the Director's complaint.
(2)
End of Assignment
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