The distribution of the number of viewers for the Malaysian Idol show follows a normal distribution with a mean of 32.5 million and a standard deviation of 6.2 million.

1. Given the probability that the average number of viewers in the next five weeks will have less than k million viewers is 3A.5%. Find the value of k. (4 marks)

1. A random sample of 3B weeks are selected, what is the probability that the average number of viewers in this sample is less than 30 million? (4 marks)

Question 2

According to a survey, 7A% of adults said that college education fee has become too expensive for most people and they cannot afford it. Suppose that this result is true for the current population. Let p be the proportion in a random sample of 1500 adults who will hold the said opinion.

1. Find the mean and standard deviation of the sample proportion.

(2 marks)

1. Find the probability that 76.B % to 78.C % of adults in this sample will hold this opinion.

(4 marks)

1. Explain central limit theorem, and show that the sampling distribution of p is approximately normal.

(3 marks)

Question 3

Almost all employees working for financial companies in KL City receive large bonuses at the end of the year. A sample of 2B employees selected from financial companies in KL showed that they received an average bonus of RM 25,000 last year with a standard deviation of RM 8,000. Construct a 95% confidence interval for the average bonus that all employees working for financial companies in KL City received last year.

(4 marks)

Question 4

An insurance company selected a sample of 50 auto claim filed and investigated those claims carefully. The company found that 1C % of those claims were fraudulent.

Construct a 99% confidence interval for the percentage of all auto claims filed with this company are fraudulent. (4 marks)

Question 5

An educator claims that the average salary of substitute teachers in school districts in Wakaf Bharu, Kelantan, is less than RM6C per day. A random sample of eight school districts is selected, and the daily salaries are shown.

6A 5B 6C 5A 7B 5C 6A 5C

1. Find the unbiased estimate for the population mean and standard deviation.

(4 marks)

1. Construct a 98% confidence interval for the population mean salary. Explain your result.

(4 marks)

1. Run a hypothesis test, is there enough evidence to support the educator's claim at =0.10?

(7 marks)

Question 6

Jenny believes that 50% of the first-time brides in Malaysia are younger than their grooms. She randomly selects a sample of 100 first-time brides and 5B reply that they are younger than their grooms.

1. Perform a hypothesis test to determine if the percentage is different from 50%, at 1% level of significance. (7 marks)

1. Explain Type I and Type II errors by using the above situation. (4 marks)

Question 7

A soft drink manufacture (Brand X) wishes to determine whether there are any differences in the proportion f three different regions (Northern, Central and Southern) in terms of favoritism of its brand compare to another competitor's brans (Brand Y). The results of a survey study on favoritism of 180 respondents were as follow:

Region

Soft drink manufacturer

Northern

Central

Southern

Brand X

49

26

55

Brand Y

21

10

19

Test at 5% significant level, using 2 distribution, whether there are any differences in the proportion of three different regions (Northern, Central and Southern) in terms of favoritism of its brand X compared to another competitor's bran, Brand B. (9 marks)