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I'm taking an online practice exam to prepare for a real test. This question appeared and I believe I'm answering it correctly but the online practice exam scoring engine keeps telling me I'm wrong, but I'm pretty sure I'm right. Here's the question:

Use the following information to determine your answers: The typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours.

About 68% of adults typically sleep between a minimum of ___ hours a night and a maximum of ____ hours a night.

Please enter your answer in the following format and round to the first decimal place: (min_value, max_value)

My answer is $(6.2,8.8)$ but I keep getting it wrong. Can someone help me understand what I'm doing wrong, or if the auto-corrector is wrong?

Thank you.

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  • $\begingroup$ it probably asks for a symmetric interval around the mean and I think you're correct considering the simplicity of the context. Try entering decimals with commas (and dots) as well. $\endgroup$
    – gunes
    Commented May 4, 2020 at 8:11
  • $\begingroup$ @gunes thanks for the insight. On other questions on this same practice exam I've used the same "." and also answered with or without the parenthesis with no luck. Maybe they have the expected answer entered on the back end, that's my best guess now. $\endgroup$
    – Python_Learner
    Commented May 4, 2020 at 10:31
  • $\begingroup$ Please add the self study tag. $\endgroup$
    – Peter Flom
    Commented May 5, 2020 at 12:03
  • $\begingroup$ @PeterFlom added tag as recommended. Thx. $\endgroup$
    – Python_Learner
    Commented May 5, 2020 at 19:08

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Comment: As @gunes comments, you have correctly found an interval that satisfies the 68% condition stated in the question---and is also symmetrical about the mean $\mu = 7.5.$ A sensible choice on your part. In R:

diff(pnorm(c(6.2,8.8), 7.5, 1.3))
[1] 0.6826895

But there are very many other intervals that satisfy the 68% criterion. For example, $(0, 8.1).$

diff(pnorm(c(0,8.1), 7.5, 1.3))
[1] 0.6777938

Perhaps yet another publisher's automated quiz program written by someone who knows very little statistics or probability. Maybe they're a CS guru, a randomly chosen high school basketball coach who sometimes teaches math, or a writer for their advertising materials.

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  • $\begingroup$ Maligned basketball coaches, advertising writers and CS gurus deserve their advocates too. $\endgroup$
    – Nick Cox
    Commented May 5, 2020 at 13:53
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    $\begingroup$ Fine people all. Just maybe not the best people to be writing statistics quiz software. $\endgroup$
    – BruceET
    Commented May 5, 2020 at 14:40

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