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Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 147?

A. 68% of the data points lie between 143 and 151.
B. 68% of the data points lie between 139 and 155.
C. 68% of the data points lie between 135 and 159.
D. 68% of the data points lie between 131 and 163.

Sagot :

GinnyAnsweridn
To determine the correct sentence describing the data set, we need to focus on the range where 68% of the data points lie in a normal distribution with the given mean (147) and standard deviation (4).

For a normal distribution:
- 68% of the data points lie within one standard deviation of the mean.

Given:
- Mean (μ) = 147
- Standard deviation (σ) = 4

Therefore, we calculate the bounds as follows:
- Lower bound = Mean - Standard deviation = 147 - 4 = 143
- Upper bound = Mean + Standard deviation = 147 + 4 = 151

Hence, 68% of the data points lie between 143 and 151.

Now, we compare this range with the given options:
O A.
68% of the data points lie between 10 and 14. (Incorrect)
O B.
68% of the data points lie between 8 and 12. (Incorrect)
О с.
68% of the data points lie between 10 and 16. (Incorrect)
O D.
68% of the data points lie between 10 and 18. (Incorrect)

None of the given options describe the correct range for 68% of the data points. The correct description should be:
68% of the data points lie between 143 and 151.
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