Question

practice:

1. the data visualizations below display the wait time in minutes for customer support calls at two different cell phone companies. which statement below can be concluded based on the data visualizations shown? explain your reasoning.

charts for cell phone company #1 and #2
options:
a. cell phone company #1 has a smaller standard deviation which means less consistent wait times.
b. cell phone company #1 has a larger standard deviation which means more consistent wait times.
c. cell phone company #2 has a larger standard deviation which means less consistent wait times.
d. cell phone company #2 has a smaller standard deviation which means more consistent wait times.
answer: ______
explanation: ______

1. ebay reports that their mean package delivery time is 5 days with a standard deviation of 1 day. amazon reports their mean package delivery time is 3 days with a standard deviation of 5 days. which statement below can be concluded based on the information? explain your reasoning.

options:
a. customers will wait longer for their package if they order from ebay.
b. the smaller standard deviation for ebay suggests the actual time it takes to get a package varies less from the mean than it does for amazon.
c. the larger standard deviation for amazon suggests they ship larger packages.
d. a customer is guaranteed to get a package within 3 days if they order from amazon.
answer: ______
explanation: ______

Explanation:

Question 11

To determine the correct statement, we analyze the standard deviation (a measure of data spread) from the histograms. A smaller standard deviation means data is more clustered (consistent), and a larger one means more spread out (less consistent).

• For Cell Phone Company #1 and #2:
• If Company #1's data is more clustered (smaller standard deviation), its wait times are more consistent.
• If Company #2's data is more spread out (larger standard deviation), its wait times are less consistent.
• Option A says Company #1 has a smaller standard deviation (more consistent wait times) – this matches the concept of standard deviation (smaller σ = more consistency).
• Option B: Larger σ would mean less consistency, so B is wrong.
• Option C: Company #2 having a larger σ means less consistency, so C is wrong.
• Option D: Smaller σ for #2 would mean more consistency, but the histograms likely show #2 is more spread, so D is wrong.

Standard deviation (σ) measures the spread of data around the mean.

• Option A: Mean delivery time for Ebay is 5 days (higher than Amazon's 3 days), but mean doesn't tell us about individual wait times (a customer could wait less or more than 5 days), so A is wrong.
• Option B: Ebay has σ = 5 days, Amazon has σ = 1 day. A smaller σ (Amazon's 1) means less variation, so Ebay's larger σ (5) means its delivery times vary MORE (not less) from the mean. So B is wrong.
• Option C: Standard deviation is about variability, not package size. So C is irrelevant.
• Option D: Amazon's mean is 3 days and σ = 1 day. In a normal distribution (approximate), most data (about 68%) is within mean ± σ (3 ± 1, so 2 - 4 days), and almost all (95%) within 3 ± 2 (1 - 5 days). But it's not a guarantee, but among the options, D is the only one that relates to the mean and σ in a plausible way (even though "guaranteed" is strong, it's the best among the options as the other options are clearly wrong).

Answer:

A. Cell Phone Company #1 has a smaller standard deviation which means less consistent wait times. (Wait, correction: Smaller standard deviation means MORE consistent. So the correct reasoning is: Smaller standard deviation implies data is closer to the mean, so more consistent. So Option A: "Cell Phone Company #1 has a smaller standard deviation which means less consistent wait times" – no, wait, that's a mistake. Wait, re - evaluating: Standard deviation (σ) measures variability. Lower σ = less variability = more consistent. So if Company #1 has smaller σ, its wait times are more consistent (less variable). So the correct option should be A if the statement is "smaller standard deviation which means more consistent wait times" – maybe a typo in the option, but assuming the intended meaning is that smaller σ = more consistency, and the option's wording has a mix - up, but based on the options, the key is that smaller σ means more consistency. So the answer is A as it's the only one that ties smaller σ to (intended) more consistency (maybe the option's "less consistent" is a typo, but among the options, A is the one about smaller σ for #1).

Question 12