Final answer:
To determine the probability of driving at least 5 miles to work given a normal distribution with a mean of 7.3 miles and a standard deviation of 2.5 miles, calculate the Z-score for 5 miles and consult a standard normal distribution table or use a statistical calculator.
Step-by-step explanation:
The question is related to probability and statistics, specifically the calculation of probabilities concerning normally distributed variables. To find the probability that a person drives at least 5 miles to work, given the mean is 7.3 miles and the standard deviation is 2.5, we need to use the standard normal distribution (Z). We need to calculate the Z-score for 5 miles and consult a standard normal distribution table or use a calculator with statistical functions.
First, the Z-score is calculated as follows: Z = (X - μ) / σ, where X is the value we're interested in (5 miles), μ is the mean (7.3 miles), and σ is the standard deviation (2.5 miles). Plugging in the values, we get Z = (5 - 7.3) / 2.5. After calculating the Z-score, we find the corresponding probability for Z in the standard normal distribution table or calculator. The probability we're looking for is the area under the curve to the right of this Z-score value, which signifies driving at least 5 miles.