Final answer:
To calculate the requested percentages, Z-scores are determined for each amount and the corresponding probabilities are obtained from a standard normal distribution table. For part (b), a Z-score of -1.95 yields about 2.52%. For part (c), Z-scores of -1.65 and 1.18 yield a range with about 73.94% of customers charging between those amounts.
Step-by-step explanation:
The question involves calculating probabilities for a normally distributed variable, which in this case is the amount charged per month on a credit card account. Since this is a typical question of a statistics course in college, we will use the Z-score formula to convert the dollar amounts into standard scores and then find the corresponding percentages.
Let's use the following information: the average amount charged is $280 per month, with a standard deviation of $20.
For part (b), to find the percentage of customers who charge less than $241 per month, first calculate the Z-score:
Z = (X - μ) / σ = ($241 - $280) / $20 = -1.95
Looking this Z-score up in a standard normal distribution table, or using statistical software, gives us a percentage. The exact percentage will vary slightly based on the source, but it should be approximately:
2.52%
For part (c), calculate the Z-scores for both $247 and $303.60:
Z₁ = ($247 - $280) / $20 = -1.65
Z₂ = ($303.60 - $280) / $20 = 1.18
Look up these Z-scores in the standard normal distribution table or calculate using technology to get two percentages and subtract the smaller from the larger to find the percentage of customers charging between $247 and $303.60.
The answer will be approximately:
73.94%