Question 1:

1.1. A manufacturer of computer chips claims that less than 10% of his products are defective. When 1,000 chips were drawn from a large production, 7.5% were found to be defective.
a) What is the population of interest? (2)
b) What is the sample? (2)
c) What is the parameter? (2)
d) What is the statistic? (2)
e) Does the value 10% refer to the parameter or to the statistic? (2)
f) Is the value 7.5% a parameter or a statistic? (2)
g) Explain briefly how the statistic can be used to make inferences about the parameter to test the claim. (2)

1.2 Briefly describe the difference between descriptive statistics and inferential statistics (6)
1.3. If it is estimated that 30% of all students who fall under the Business and Management Sciences Faculty at Richfield have a valid driver’s license. What is the probability that in a sample of 10 students:

1.3.1. Exactly 4 have a valid driver’s license? (3)
1.3.2. At least 2 have a valid driver’s license? (3)
1.3.3. More than 9 have a valid driver’s license? (4)

Question 2:

2.A batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours. Assuming a normal distribution:

How many lamps will fail before 900 hours? (10)

How many lamps will fail between 950 and 1000 hours? (10)

And given the same mean life, what would the standard deviation have to be to ensure that not more than 20% of lamps fail before 916 hours? (10)

Question 3:

3. Researchers at the European Centre for road Safety Testing are trying to find out how the age of cars affects their braking capability. They test a group of ten cars of differing ages and find out the minimum stopping distances that the cars can achieve. The results are set out in the table below:

 car Age (months) Minimum stopping at40 km per hour A 9 28.4 B 45 29.3 C 24 37.6 D 30 36.2 E 38 36.5 F 46 35.3 G 53 36.2 H 60 44.1 I 64 44.8 J 76 47.2

Using information provided above to answer the following questions:

Draw a scatter diagram from the data. (15)

Compute Spearman’s correlation coefficient (rho) (15)