# BAMS1743 : JUNE 2023- Quantitative Methods, Assignment , TAR UMT, Malaysia

University |
Tunku Abdul Rahman University of Management and Technology (TAR UMT) |

Subject |
BAMS1743 : Quantitative Methods |

**Question 1**

**a) The following data shows the grade point average (GPA) obtained by 9 students in the last semester:**

1.92Â Â 2.67Â Â 2.75Â Â Â 2.98Â Â 3.33Â Â Â 3.50Â Â 3.88Â Â 3.96Â Â Â 4.00

(i) State the variable of interest. Indicate whether this variable is a quantitative discrete, quantitative continuous, or qualitative variable.

(ii) Calculate the inter-quartile range.

**b) The following frequency table shows the grade point average (GPA) obtained by a random sample of 80 business students last semester.**

(i) Calculate the mean and the standard deviation of the above data.

(ii) Calculate the mean and the standard deviation of the above data. (7 marks)

The mean and standard deviation for the grade point average for a group of engineering students were 2.96 and 0.92 respectively. Calculate the coefficients of variation for the two distributions and comment on the results.

(iii) Construct a histogram for the frequency distribution.

(iv) Estimate the mode from your histogram and interpret the result.

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**Question 2**

**a) The following contingency table shows the problem-solving skills of a random sample of 400 students from three different programs.**

(i) A student is selected randomly. Find the probability that

(1) the student is from the Event Management program and he/she possesses good problem-solving skills.

(2) the student possesses poor problem-solving skill given that he/she is from Gastropreneurship program.

(ii) Are the events ‘Tourism Management’ and ‘Good problem-solving skill’ independent? Justify your answer.

**b) A record shows that 15% of the SPM top scorers will be offered scholarships to further their studies. If 50 SPM top scorers are chosen randomly,**

(i)calculate the mean and the standard deviation of the number of SPM top scorers who will be offered the scholarship.

(ii) calculate the probability that at least 10 SPM top scorers will be offered the

scholarship.

**c) The masses of jackfruits are distributed normally with a mean of 8.5kg and a standard deviation of h kg. Jackfruit is graded according to its mass. The minimum mass of a grade A jackfruit is 10 kg.**

(i) Find the standard deviation, h corrects to 3 decimal places if 35% of the jackfruits are grade A jackfruits.

(ii) Use the standard deviation obtained in Question 2 c) (i), find the probability of getting a jackfruit with a mass of more than 8.45kg.

**d) The average number of defective items produced by a machine is 5 in every 30 minutes. Assume that the number of defective items produced follows a Poisson distribution. Find the probability that the machine produces at most three defective items in the next one hour.**

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**Question 3**

**a) The following table shows the internship evaluation score given by a supervisor and the absenteeism record from a random sample of 8 students last semester.**

(i) Calculate the product moment correlation coefficient.

(ii) Find the least squares regression equation of the evaluation score on absenteeism.

(iii) By using the regression equation, estimate the evaluation score if the number of absences is seven days. Comment on the reliability of the estimation.

**b) The daily production of (‘000 units) of light-emitting diode (LED) lightbulbs over the past three weeks are given below:**

(i) Obtain a suitable moving average trend.

(ii) Calculate the average seasonal variations for the daily production using the additive model.

(iii) Forecast the production for Tuesday of the following week.

**Question 4**

**a)** Last semester, a group of 24 out of 80 students obtained more than 3.50 GPA. Construct a 96% confidence interval for the true proportion of all students who obtained more than 3.50 GPA.

**b)** A lecturer claimed that the GPA for business students is below 3.00. A random sample of 100 students were taken and found that the mean and standard deviation of the GPA were 2.95 and 0.7 respectively. Test at 5% significant level whether the claim is valid.

**c)** Mr. Ben obtained a loan of RM400,000 from a bank for 18 years. The interest rate is 3.96% per annum compounded monthly. Find the monthly installment if the first installment is paid one month after the loan being released.

**d) A company is considering a project with the cash inflows and outflows as tabulated below:**

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