STRUCTUREDQUESTION [Total = 100marks]

Answer ALLquestions.

Question 1 [20marks]

(A) The following data represent the price (in sen) of 100 grams of chilli in the supermarket for 20 consecutivedays.

50 63 58 64 71 46 75 49 67 61

48 58 62 70 59 53 66 49 58 60

(i) Compute the measurement of centraltendency.

(ii) Compute the variance and standarddeviation.

(6marks)

(6marks)

(B) The causes for late on differentoccasions.

Causes for Late Arrival	Number of Occasions
Family problems	6
Had to take the bus	4
Woke up late	30
Bad weather	5
Sick	8
Traffic tied-up	24

Make a pie chart for these data.

(8marks)

Question 2 [20marks]

(A) The probability that boards purchased by a cabinet manufacturer are unusable for building cabinets is 0.15. The cabinet manufacturer bought twentyboards.

(i) Find the mean and standard deviation of unusableboards.

(3 marks)

(ii) Find the probability that at most two of the twenty boards are unusable for building cabinets.

(5 marks)

(B) An average of 5 calls for service per day are received by a technician. In a randomly selected day, find the probabilitythat

(i) exactly two calls for service will bereceived.

(ii) more than one call for service will bereceived.

(3marks)

(5marks)

(C) At a certain community college, the time that is required by candidates to complete the general knowledge competency examination is normally distributed with a mean of 57.5 minutesandastandarddeviationof6minutes.Findtheprobabilitythatacandidatetakes between 56 minutes and 1 hour to complete theexamination.

(4 marks)

Question 3 [20 marks]

(A) The mean wage for all 5500 employees who work at a large company is RM12.50 per hour and the standard deviation is RM1.70 per hour. Let be the mean wage per hourfor a random sample of certain employees selected from this company. Find the mean and standard deviation of for a sample size of50.

(3 marks)

(B) A sample of 1500 cakes sold recently in a bakery gave the mean price of cakes equal to RM60.40. The population standard deviation of the prices of cakes in this bakery is RM3.50. Construct a 95% confidence interval for the mean price of all cakes in this bakery.

(7 marks)

(C) A random sample of eleven packages was selected from a machine packaging sugar in packages marked 500g. The actual weights of salt in kgwere:

498 502 503 504 495 499 501 498 500 499 503

Assuming that the weights are normally distributed, calculate a 95% confidence interval for the mean weight of salt in packages marked 500g.

(10 marks)

Question 4 [20marks]

(A) A lecturer claims that students in Economy class put more hours studying compared to other students. The mean numbers of hour spent studying per week is 24hours with a standard deviation of 3.5 hours per week. A sample of 35 Economy class students was selected at random and the mean number of hours spent studying per week was found to be 25 hours. Determine the lecturer's claim can be accepted at 5% significancelevel.

(9 marks)

(B) Abu packs sweets and sell them in a packet of 100g each. Twelve randomly selected packets of sweets are taken and their weights in grams are recorded asfollows:

98 100 94 96 97 95 100 102 101 97 103 99

Perform the required hypothesis test at 5% significance level to check whether the mean weight per packet of sweets is not equal to 100g.

(11 marks)

Question 5 [20marks]

Acompanymanufacturesagadgettobeusedinaverywidetemperaturerange.Thecompany knows that increased temperature shortens the lifetime of the device, and a study is therefore performed in which the lifetime is determined as a function of temperature. The following data isfound.

Temperature (C)	Lifetime (hours)
10	380
21	316
30	265
42	202
53	174
62	113
70	66
81	35
92	9

(A) Construct a linear regression model for the givendata.

(6 marks)

(B) Interpret the relationship between temperature and lifetime of thegadget.

(4 marks)

(C) Estimate the lifetime of the device given temperature of1C.

(3 marks)

(D) Obtain the correlation coefficientvalue.

(5 marks)

(E) Interpret the value of correlationcoefficient.

(2 marks)