Question 1

a. During Movement Control Order (MCO), a pharmacy located in a shopping mall found that35% of their customers purchase products through online shopping.

(i) A random sample of 8 customers is selected. Determine the probability that morethan 6 customers purchase products using online shopping. (3 marks)

(ii) Determine the probability that, in a random sample of 50 customers, the number ofcustomers purchasing products online are between 15 to 20 customers inclusively.(4 marks)

b. In an hour, an average of 10 customers arriving at a shopping mall entrance during theMovement Control Order (MCO). If the arrival of the customers at the shopping mall entrancefollows Poisson distribution. Determine the probability that exactly 5 customers arriving from10 am to 11 am at a shopping mall entrance during MCO. (2 marks)

c. The price of a bottle of vitamin C is normally distributed with a mean of RM36.50 and astandard deviation of RM0.50.

(i) What is the percentage that the price of a bottle of vitamin C is between RM36 and RM37? (3 marks)

(ii) 95% of the selling price for a bottle of vitamin C is below RM k, find the value of k. (3 marks)

Question 2

The pharmacist records the daily earning (in RM) from the sales of vitamin C during the MCO of14 days, 6 days without any sales of vitamin C. The earnings from the sales of vitamin C for theother 8 days are shown below:-

131 143 183 196 153 137 105 142

a. Calculate the mean and interpret. (2 marks)

b. Find the population standard deviation. (3 marks)

Question 3

The pharmacist wants to estimate the true average daily earning (in RM) from the sales of vitaminC based on 95% confidence level. A random sample of 30 days of record with an average dailyearning of RM85 and a standard deviation of RM76.40.

a. Calculate the interval estimate of the true average daily earnings from the sales of vitamin C.(2 marks)

b. The pharmacist wants the estimate of the average daily earning with at most RM20 differences from the true mean. Based on 95% confidence level, do you think that thepharmacist has enough records? How many days of records should the pharmacist collect?Justify. (3 marks)