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A shelter has 24 dogs up for adoption. Suppose you want to adopt 2 of them....

  1. A shelter has 24 dogs up for adoption. Suppose you want to adopt 2 of them. How many different ways could you choose 2 dogs from the 24?  

  1. We are interested in analyzing data from bike sharing in LA. Use O to denote a one-way route and A to denote an annual pass. The probability that someone has a one-way trip route is 84.74%. The probability that they have an annual pass is 2.77%. The probability that they have an annual pass and took a one-way trip route is 2.7%.

  1. What percentage of people take a one-way trip or have an annual pass?

  1. What percentage of people take a two-way trip route?

  1. Given someone has an annual pass, what is the probability that they took a one-way trip?

  1. What percentage of people do NOT take a one-way trip route NOR have an annual pass?

  1. Are O and A mutually exclusive events? Why or why not?

  1. Are O and A independent events? Explain, using probabilities.

  1. If we know someone took a one-way trip, what is the probability they have an annual pass?

  1. Building off of question 2, we know that 58% of trips are 15 minutes or less. Suppose we take a sample of 10 trips.

  1. How many rides out of the 10 are expected to be 15 minutes or less?

  1. What is the standard deviation?

  1. What is the probability that exactly 2 of the rides are 15 minutes or less?

  1. What is the probability that more than 2 of the rides are 15 minutes or less?

  1. The following information was gathered about the time of the rides for the bike share data.

Ride Time

Frequency

1 Minute

955

5 Minutes

4436

10 Minutes

3016

15 Minutes

1887

a. Find the average ride time.

b. Find the standard deviation of this distribution.

  1. Assume we are interested in looking at GRE scores of students admitted to graduate schools. Suppose GRE scores are Normally distributed with an average of 317 and a standard deviation of 11.5 points. Suppose we take a sample of 15 admitted students.

  1. What is the probability that a randomly selected student will have a GRE score above 325?

  1. What is the probability that a randomly selected student will have a GRE score under 312?

  1. What is the probability that a randomly selected student will have a GRE score between 310 and 320?

  1. What is the probability that the average GRE score from our sample of 15 students will be above 320?

  1. What score defines the lowest 7.93% of the distribution for an individual student?  

  1. What score defines the highest 34.09% of the distribution for an individual student?

  1. Suppose we go back to the example from question 3. Suppose the probability remains at 58% but we now take a sample of size 200.

  1. What is the standard error of the proportion?

  1. What is the probability that the sample proportion of ride times 15 minutes or less will be between 53% and 60%?

  1. Two estimates are available for the same population parameter. Estimate one has a standard deviation of 4.6 and estimate two has a standard deviation of 4.7. Estimate two is not consistent, whereas estimate one is consistent. Which estimate would you choose and why? Could anything else affect this decision?

  1. Suppose I want to survey a group of students about their thoughts on online classes. I decide to look at all 5 of my classes, online or in person. I take a random sample of 15 students from each course and survey them. What type of sampling method am I using?

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