Math Problem with Standard deviation and Expected Time

Question

A survey was done on a group of people that asked the time, , it takes them to commute to work, rounded to the nearest 10 minutes. Use the probability distribution table below to answer Part 1-2.

X P(X=x)

0 0.125

10 0.221

20 ____

30 0.165

40 0.098

50 0.024

Part 1: Calculate the expected time for a person to commute to work.

Part 2: Calculate the standard deviation for the time it takes a person to commute to work.

Answer 1

It would help if you submit some work on the problem. I will get you started.

In part 1, first find the missing probability for 20. What do the six probabilities in the table have to add up to? 1. So subtract 1 - the total of the other 5 probabilities to get the probability for 20. Then multiply each outcome times its probability and add all the products up to get the expected value.

In part 2, there are four steps to finding the standard deviation of random variables. First, calculate the expected mean time (done in part 1). Second, for each value in the group (0, 10, 20, 30, 40, 50) subtract the mean and multiply the result by the probability of that outcome occurring. Third, add the six results together. Fourth, find the square root of the result.

After you work on this, you may submit your work with further questions or to be checked.