Watching Television The amount of time Americans spend watchin...

Name: A survey asks employees about their 'daily commute time in minutes.' Would
Uploaded: 2025-11-24T02:23:37.433Z
Duration: 4 min 55 s
Description: Watch the video explanation for the concept: A survey asks employees about their 'daily commute time in minutes.' Would

Question

Watching Television The amount of time Americans spend watching television is closely monitored by firms such as AC Nielsen because this helps determine advertising pricing for commercials.

a. Do you think the variable “weekly time spent watching television” would be normally distributed? If not, what shape would you expect the variable to have?

Accepted Answer

Welcome back everyone. In this problem, a survey asks employees about their daily commute time and minutes. Would you expect the distribution of this variable to be normal? If not, what shape would it most likely have? A says yes, it would be normally distributed. B, no, it would be likely left skewed. No, it would likely be right skewed, and D, yes, it would be uniform. Now let's try to figure out the the answer to this first question. Do we expect the distribution of this variable to be normal? Well, what does a normal distribution look like? Will recall that in a normal distribution. It represents a variable that is symmetrical or or its measure is symmetrical above the mean. OK? So if we have our mean here, OK, for our distribution, then it's normal if the side on the left of the mean mirrors the side on the right of the mean. So for us to figure out if this variable is normal, we need to ask ourselves, what do we know about commute time in minutes. Well if we think about it, for starters, we know that commute time. OK, commute time cannot be negative. And that's really important here because that creates a hard physical limit at 0 minutes which immediately prevents the distribution from being perfectly symmetrical. That means the data points are forced to pile up near this lower boundary of zero minutes. So, for example, here, if we have our 0 minutes at this point, then it would have to be symmetrical here for it to be considered normal. Thus this tells us that our distribution would not be normal. No, because of that, we we have to ask ourselves what shape would it most likely have. Well, if we think about it, the majority of employees are incentivized to live relatively close to their workplace or they use efficient direct routes. This means the mode, that is the most frequent commute time, OK, the mode. And the bulk of the data. Will occur. At the lower end. OK. Of the time scale. So what does that mean? Well, That means that if we were to put our distribution here and put our start at 0 minutes or high start of 0, most of our values, like we said, would be the mode would be close to this lower end, right? So we'd probably have our mode somewhere here and most of our values would be in this area. But now, if we think about it, while short times are common, there is no realistic upper limit on how long a commute can be. A few employees might live far away, rely on multiple modes of transport, or face unpredictable congestion. So these few very long commute times will form a long, sparse tail to the right of the distribution. So it would probably look something like this. Now, this is a right skewed distribution. Because here our tail is skewed or pulled to the right. Now in a rescue distribution, most employees, that is the bulk of the data, will have commute times less than the average mean time. The mean is also sensitive to extreme values, so the long high values in the right tail pull the mean in that direction. However, the median is resistant to out layers, so it remains clustered with the majority of the data. So for this distribution for the commute time, the mode will be less than the median. And the median will be less than the mean. And this relationship where the average is higher than the median is the definitive statistical evidence that the distribution is right skewed or positively skewed. Therefore, if we look back at our answer choices, our distribution is not normal, but instead would likely be right skewed. Thanks a lot for watching everyone. I hope that I hope this helps. Thus, the correct answer is C.

Key Concepts

Normal Distribution

Skewness and Distribution Shape

Real-World Data Characteristics

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