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Probability of Machine being Tuned and Serviced

Question 1:
A sensitive machine is tuned correctly for 95% of the time. If the machine is correctly tuned, the probability of spoil product is 1% if not is 40%. The first product of a test run is inspected and found to be satisfactory.

What is the probability that the machine had been correctly tuned?

Question 2
The service of time of a new BMW is found to be normally distributed with a mean of 70min and a variance of 81min2
1: If the customer brings her BMW car for the first service what is the probability that the car will be ready within 1 Hour.
2: What is the probability that the job will take more than 90min.
3: What is the percentage of the first service will be completed between 50min and 60min.
4: The BMW dealer has a policy to give its customers a 15% discount on the cost if the service is not completed within 80min. From a sample of 80 customers who brought their cars in for the first service, how many are likely to receive the 15% discount?
5: If the dealer wants to ensure that no more than 5% of all its first service will take longer than 80min, what should the mean service time be?

Solution Summary

The probability of a machine being tuned and serviced is determined in the solution.