Final answer:
The probability that a computer is assembled in a time between 45 and 60 minutes, with assembly times normally distributed and a mean of 50 and standard deviation of 10 minutes, is about 53.28%.
Step-by-step explanation:
The question asks us to calculate the probability that a computer is assembled in a time between 45 and 60 minutes, given that the time to assemble a computer is normally distributed with a mean of 50 minutes and a standard deviation of 10 minutes.
To find this probability, we would use the standard normal distribution (Z-scores). We first need to convert our time values into Z-scores using the formula Z = (X - mean) / standard deviation. So for 45 minutes, the Z-score would be (45 - 50) / 10 = -0.5, and for 60 minutes, the Z-score would be (60 - 50) / 10 = 1.0.
Next, we look up these Z-scores on a standard normal distribution table or use a calculator with statistical functions to find the probabilities corresponding to these Z-scores. The probability of being between the two values is the difference between the probabilities associated with each individual Z-score.
Assuming a standard normal distribution table, the area under the curve to the left of Z = -0.5 might be around 0.3085, and for Z = 1.0 it might be around 0.8413. Therefore, we subtract the smaller area from the larger area to find the probability of assembly time being between 45 and 60 minutes:
Probability = P(Z < 1.0) - P(Z < -0.5) = 0.8413 - 0.3085 = 0.5328
Thus, the probability that a computer is assembled in a time between 45 and 60 minutes is approximately 53.28%.