Final answer:
To find the percentage of Jen's phone bills between $43 and $97, calculate the z-scores for both amounts and refer to the normal distribution. Approximately 99.7% of data falls within three standard deviations from the mean, so about 99.7% of her phone bills fall between these two amounts. Therefore, the correct answer is option D) Approximately 99.7%.
Step-by-step explanation:
The question involves the concept of the normal distribution of Jen's monthly phone bill, which is characterized by a mean (μ) of $70 and a standard deviation (σ) of $9. To determine the percentage of her phone bills that are between $43 and $97, we have to calculate the z-scores for these two amounts and then refer to the standard normal distribution table or use a statistical tool to find the corresponding percentages.
The z-score formula is z = (X - μ) / σ, where X is the value for which we are calculating the z-score. For $43:
z = ($43 - $70) / $9
= -3
For $97:
z = ($97 - $70) / $9
= 3
According to the properties of the normal distribution, approximately 99.7% of data falls within three standard deviations from the mean. Therefore, the answer is:
D) Approximately 99.7%