Final answer:
The z-score for company N's operating expenses ($37.42) against the mean ($29.78) with a standard deviation of $2.75 is 2.78. Using a standard normal distribution table, it's found that about 0.5% of regional phone companies had higher operating expenses than company N.
Step-by-step explanation:
To estimate the percentage of regional phone companies whose operating expenses were higher than those of company N, we need to calculate the z-score and then find the corresponding percentage from the standard normal distribution table.
The z-score is given by the formula:
Z = (X - µ) / σ
Where:
- Z is the z-score,
- X is the value from the data set,
- µ is the mean of the data set,
- σ is the standard deviation of the data set.
For company N:
Z = (37.42 - 29.78) / 2.75
Z = 7.64 / 2.75
Z = 2.78
After calculating the z-score, we look up this value in a standard normal distribution table, or we can use a calculator that provides the cumulative distribution function for a standard normal distribution to find the percentage of companies with higher operating expenses than company N. This would be the area to the right of the z-score in the standard normal distribution.
Looking at a z-table or using a calculator, we find that the area to the right of a z-score of 2.78 is approximately 0.5%. Therefore, we estimate that 0.5% of regional phone companies had higher operating expenses than company N during the first half of 1994.