High School

Your sample is normally distributed with a mean temperature of 98.3 degrees. The standard deviation in this sample is 0.8 degrees. You would expect:

A. Most of the temperatures to be close to 98.3 degrees.
B. A wide range of temperatures in the sample.
C. All temperatures to be exactly 98.3 degrees.
D. The standard deviation to be negative.

Answer :

Final answer:

For a normally distributed sample with a mean of 98.3 and a standard deviation of 0.8, most data points are expected to be close to the mean, with a not too wide range due to the low standard deviation, and some slight variations around the mean. A negative standard deviation is impossible.

Explanation:

The question is asking about the characteristics of a normally distributed sample with a mean temperature of 98.3 degrees and a standard deviation of 0.8 degrees. In a normal distribution:

  1. We would expect most of the temperatures to be close to the mean (98.3 degrees). This is due to the nature of a normal distribution, where most data lies close to the mean.
  2. We wouldn't expect a wide range of temperatures as the standard deviation (0.8) is relatively low. A low standard deviation means that most of the data points are close to the mean.
  3. All temperatures would not be exactly 98.3 degrees. While the mean is 98.3, a normal distribution would include temperatures a bit lower and a bit higher than the mean.
  4. The standard deviation cannot be negative. It is a measure of variability, and can be either positive or zero, never negative.

In summary, for a normal distribution with a specific mean and standard deviation, the majority of data is expected to be near the mean with slight variations according to the standard deviation.

Learn more about Normal Distribution here:

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