Question

uber rides 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. use the standard normal distribution table. round the final answers to at least four decimal places, and intermediate z value calculations to two decimal places. your answer part 1 of 3 (a) between 28 and 40 rides per week. ( p(28<x<40)= ) 0.5328 part 2 of 3 (b) more than 33 rides per week. ( p(x>33)= ) 0.6480 part: ( 2 / 3 ) part 3 of 3 (c) less than 32 rides per week. ( p(x<32)= ) 0.9772

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(\mu = 36\) (mean) and \(\sigma=8\) (standard deviation).
For \(x = 32\), \(z=\frac{32 - 36}{8}=\frac{-4}{8}=- 0.5\)

Step2: Find the probability using the standard normal distribution table

We want to find \(P(X < 32)\), which is equivalent to \(P(Z<-0.5)\)
Looking up the value of \(z=-0.5\) in the standard normal distribution table. The value corresponding to \(z =-0.5\) is \(0.3085\)

Answer:

\(0.3085\)