What would be the average number of defective components

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Reference no: EM132372686

Business Statistics Assignment -

The purpose of an assignment is to ensure that the Learner is able to:

make informed decisions based on data.
correctly apply a variety of statistical procedures and tests.
know the uses, capabilities and limitations of various statistical procedures.
interpret the results of statistical procedures and tests.

QUESTION ONE -

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

1.1.1 how many lamps will fail before 900 hours?

1.1.2 how many lamps will fail between 950 and 1000 hours?

1.1.3 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?

1.2 Components are placed into bins containing 100. After inspection of a large number of bins the average number of defective parts was found to be 10 with a standard deviation of 3. Assuming that the same production conditions continue, except that bins containing 300 were used:

1.2.1 what would be the average number of defective components per larger bin?

1.2.2 what would be the standard deviation of the number of defectives per larger bin?

1.2.3 how many components must each bin hold so that the standard deviation of the number of defective components is equal to 1% of the total number of components in the bin?

QUESTION TWO -

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 at 40 kilometres per hour (metres)
A	9	28.4
B	15	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:

2.1 Draw a scatter diagram from the data.

2.2 Compute Spearman's correlation coefficient (rho).

2.3 Compute Pearson's correlation coefficient(r).

QUESTION THREE -

3.1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers:

3.1.1 Exactly 4 will have a medical aid.

3.1.2 At least 2 will have a medical aid.

3.1.3 More than 9 will have a medical aid.

3.2 Sun Couriers, a parcel delivery company, has found that the delivery time of parcels to clients in the Durban metropolitan area after airport collection is normally distributed with a mean delivery time equal 45minutes (µ = 45) and a standard deviation of 8 minutes (α=8).

For a newly arrived consignment at Durban airport, what is the probability that a randomly selected parcel will take: Between 45 and 51 minutes to deliver to the client.

Reference no: EM132372686

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