Question

In a large city, the average number of rides an Uber driver makes in a week is 36. Assume the distribution is approximately normally distributed and the standard deviation is 8. Find these probabilities for the rides a randomly selected Uber driver makes in a week. Round the final answers to at least four decimal places, and intermediate z value calculations to two decimal places.

Answer 1

The question asks for calculating probabilities using a normal distribution given the mean and standard deviation of the number of rides an Uber driver makes in a week.

Step-by-step explanation:

The question pertains to probability and statistics, specifically focusing on the normal distribution and calculating probabilities. The situation described involves the average number of rides an Uber driver makes in a week. To find the required probabilities, we use the properties of the normal distribution along with the provided mean and standard deviation.

To calculate probabilities for a normally distributed random variable, we first convert the number of rides to a z-score. The formula for the z-score is z = (X - μ) / σ, where X is the value for which we are finding the probability, μ is the mean, and σ is the standard deviation. Once we have the z-score, we can use standard normal distribution tables or software to find the probabilities.

Here are the steps for each part:

1. Calculate the z-score for each value.
2. Use the z-score to find the probability associated with each value.
3. Interpret the results of the probabilities in the context of the problem.

It's important to use a calculator or software for exact probability calculations and round final answers to at least four decimal places.