Final answer:
The question involves calculating the probability of receiving at most 46 service calls per hour using the normal approximation to the Poisson distribution, given an average of 55 calls per hour.
Step-by-step explanation:
The student's question is about using the normal approximation to the Poisson distribution to find the probability of an electric company receiving at most 46 service calls per hour when the average arrival rate is 55 per hour. To solve this using normal approximation, we first need to find the mean (μ) and the standard deviation (σ) of the Poisson distribution. The mean is μ = 55, and the standard deviation is σ = √55, as it is the square root of the mean for a Poisson distribution.
Next, we convert the Poisson distribution to a normal distribution using these parameters. Now we normalize the value for which we're finding the probability (46 calls). The z-score is calculated using the formula z = (X - μ) / σ, where X is the number of service calls.
After obtaining the z-score, we use the standard normal distribution table or a calculator to find the probability of having a z-score less than or equal to the calculated value. The final probability rounded to four decimal places would be the answer to the student's question.