Question 6

A pencil box consists of three types of pen, X, Y and Z in the ration 2:1:7. A sample of 5 pen is chosen from the pencil box. Determine the probability that

(a)less than one pen of type X have been chosen.(2 marks)

(b)more than one pen of type Y have been chosen.(2 marks)

(c)at least 1 pen of type Z have been chosen.(2 marks)

Question 7

A company that manages toll services found that the number of vehicles arriving at a particular toll plaza between the hours of 10.00 and 11.00 in the morning each day has a Poisson distribution with the mean of three cars per minute. Find the probability that the number of vehicles arriving at anyone minutes is

(a)at most 2.(3 marks)

(b)at least 2.(3 marks)

Question 8

The heights of boys at a particular age follow a normal distribution with mean 150.3cm and standard deviation 5cm. A boy is picked at random from this age group.

(a)Find the probability that he has height less than 148cm. (2 marks)

(b)Find the probability that he has height between 147 cm and 149.5 cm.

(2 marks)

(c)The percentage of boys who has height less than k cm is 64%. What is the value of k. (3 marks)

Question 9

An insurance company selected a sample of 50 auto claim filed with it and investigated those claims carefully. The company found that 12% of those claims were fraudulent.

(a)What is the point estimate of the percentage of all auto claims filed with this company that are fraudulent?(2 marks)

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

Question 10

An educator claims that the average salary of substitute teachers in school districts in Wakaf Bharu, Kelantan, is less than RM60 per day. A random sample of eight school districts is selected, and the daily salaries are shown. Is there enough evidence to support the educator's claim at ?

6056605570556055(5 marks)