RECENT ASSIGNMENT

QUESTION 2 Statistical Decision Making and Quality Control
Show all calculations/reason
(a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past, the mean time has been 45 minutes with a standard deviation of 15 minutes and is believed to be normally distributed. The company proposes to collect random samples of 36 observations to monitor labour time.
1. If management wishes to establish x ¯ control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.
2. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. (Round calculations to 2 decimal places)
(b) Quality control chart
Using the Excel Chart function prepare a quality control chart from the following sequential monthly cycle time data. The desired level of performance is 140, with an upper control limit of 160 and a lower control limit of 120.

Month
Average Cycle Time
(Hours)
January
124
February
175
March
147
April
97
May
153
June
132
July
228
August
152
September
172
October
112
November
138
December
141
Explain whether the process is in control or whether corrective action is required.
Justify your conclusion.
(d) An urn contains 20 marbles. 6 are red, 10 are green and 4 are blue. Marbles are drawn and then replaced after each draw.
Calculate the probability of drawing:
(i) a blue marble on the first draw
(ii) a blue marble on the first draw and a red on the second draw
(iii) two green marbles in two draws
(iv) red marble on the second draw given a blue on the first draw
(e) The time to complete a construction project is normally distributed with a mean of 80 weeks and a standard deviation 8 weeks.
(i) What is the probability that the project will be completed in 84 weeks or less?
(ii) What is the probability that the project will be completed in 92 weeks or less?
(iii) What is the probability that the project will take longer than 90 weeks?
Rationale
This assessment task covers topics 1 and 2: Probability concepts and distributions, and Statistical decision making and quality control. It has been designed to ensure that you are engaging with the subject content. More specifically, it seeks to assess your ability to:
apply probability concepts to decision making
demonstrate problem solving skills in assessing, organising, summarising and interpreting relevant information for decision making
demonstrate understanding of the application of statistical hypothesis testing to decisions, with particular emphasis on quality control