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Which of the following describes a set of data whose histogram approximates a normal curve?. . check all that apply . . A. The histogram of the data is exactly the same as the normal curve.. B. The observations trail off at values far from the mean.. C. All of the data values have to be positive.. D. Most of the observations are near the mean of the data set.. E. The sum of the data values must be 1.

Verified Answer :

Answer:

the answer is D and B

Step-by-step explanation:

APEX

Answer:

The correct options are B and D.

Step-by-step explanation:

It is provided that the histogram of a data set approximates a normal curve.

In case of a normal curve:

  1. The mean, median and mode of the data set are equal and are the central point of the distribution.
  2. The shape of the curve is bell-shaped or symmetric, i.e. on dividing the curve in half one side is the mirror image of the other side.
  3. The total area under the normal curve is 1.
  4. In a normal curve 68.26% of the data lies under 1σ of mean, 95% lie under 2σ of mean and 99.73% lies under 3σ of mean.

The 4th point implies that most of the data are closer to the mean of the distribution (μ).

So, if the data mentioned has a histogram that approximates a normal curve then,

  • The histogram is almost like a normal curve.
  • The data points trail off far from mean according to the 68.26-95-99.73 rule.
  • And most of the data, i.e 99.73%, are closer to the mean.

Thus, the options that apply are B and D.

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