The life time of the Tuff brand of tyres is approximately normally distributed....

Malual90

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The life time of the Tuff brand of tyres is approximately normally distributed, with a mean of 63,000 km and a standard deviation of 3,000 km. The tyres carry a warranty of 55,000 km.
What proportion of tyres will fail before the warranty expires?
An appropriate, well labelled diagram
must be included.

The Tuff company claims that at least 10% of the tyres last longer than 68,000 km.
Provide evidence to support or disprove this statement.
An appropriate, well labelled diagram
must be included.

Second Question


A switch board operator receives an average of 25 calls every 15 minutes. Calls are received randomly and independently. The switch board operator used the following Excel command to determine a probability 1-POISSON(20, 25, TRUE .
Describe in words or write down using probability notation what probability he worked out in the context of this problem and then use Excel to evaluate it.


 
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So far I have done
Question I

proportion of tyres that will fail before warranty

Mean = 63000KM
Standard Deviation 3000KM
warranty 55000 Km

Z= 63000-55000/3000 gives me 2.67 on Z table is 0.9962.

I minus 1-0.99632 =0.0338 stuck on the diagram plus need correction on this question.

second part


P(Z>68000)
P(68000-63000)/3000= 1.67 round off on Z table is 0.9515.... i need correction as well as support statement to prove this.


Last question am not sure what am ask to do....
 
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