Final answer:
The probability that the mechanic's estimation about fixing the car engine in a maximum of 1 hour does not happen is approximately 0.82%.
Step-by-step explanation:
The question asks for the probability that the mechanic's estimation of fixing a car engine in a maximum of 1 hour does not happen. Given that the time required to fix the engine is normally distributed with a mean (μ) of 48 minutes and standard deviation (σ) of 5 minutes, we can translate the maximum time of 1 hour, which is 60 minutes, into a z-score. A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean.
To calculate the z-score for 60 minutes, we use the formula: z = (X - μ) / σ. Plugging in our values, we get z = (60 - 48) / 5 = 12 / 5 = 2.4. We then look up the z-score in the standard normal distribution table or use a calculator with normal distribution functions to find the probability of a time less than 60 minutes. To find the probability that it takes more than 60 minutes (the mechanic's estimate does not happen) we need to calculate 1 minus the probability of z being less than 2.4.
The standard normal distribution table or calculator will show that the probability of z being less than 2.4 is approximately 0.9918. Therefore, the probability that it takes more than 60 minutes, which is the complement, would be 1 - 0.9918 = 0.0082 or 0.82%.