Final answer:
To determine the fraction of calls lasting between 4.50 and 5.30 minutes, convert the call times to z-scores and find the associated probabilities.
Step-by-step explanation:
To find the fraction of calls that last between 4.50 and 5.30 minutes, given that call lengths at General Electric Corporate Headquarters follow a normal distribution with a mean of 4.50 minutes and a standard deviation of 0.70 minutes, one would use the standard normal distribution to calculate this probability.
Firstly, we convert the call lengths into z-scores using the formula Z = (X - μ) / σ, where X is the call length, μ is the mean, and σ is the standard deviation. For the lower limit (X = 4.50 minutes), the z-score is (4.50 - 4.50) / 0.70 = 0. For the upper limit (X = 5.30 minutes), the z-score is (5.30 - 4.50) / 0.70 ≈ 1.14.
Next, one would look up these z-scores on a standard normal distribution table or use a statistical software to find the probabilities associated with each z-score. The probability of a call lasting less than the mean is 0.5 (since it's the mean value on a symmetric distribution). To find the probability of a call lasting less than 5.30 minutes, we look up the z-score of 1.14 which gives us a probability of approximately 0.8729.
The difference between these two probabilities, 0.8729 - 0.5, gives us the fraction of calls that last between 4.50 and 5.30 minutes. Thus, approximately 37.29% of calls last between these times.