If data on variable is distributed normally with a mean 20 and standard deviation 4, the probability that the variable lies between 16 and 24 is:

Correct option is B

Explanation:
In a normal distribution, about 68% of the data lies within ±1 standard deviation from the mean.
· Given: Mean (μ) = 20 Standard Deviation (σ) = 4
· 1 standard deviation below the mean: 20 – 4 = 16
· 1 standard deviation above the mean: 20 + 4 = 24
So, the range 16 to 24 is within ±1σ, which includes ~68% of the total data in a standard normal distribution.
Information Booster:
In a standard normal distribution:
· ~68% of data lies within ±1σ (μ ± σ)
· ~95% of data lies within ±2σ (μ ± 2σ)
· ~99.7% of data lies within ±3σ (μ ± 3σ)
These are known as the Empirical Rule or 68–95–99.7 Rule.
Additional Information:
· Option (1): ~0.5 corresponds to the area from the mean to 1σ in one direction, not both.
· Option (3): ~0.80 represents an interval wider than ±1σ.
· Option (4): ~0.95 is the probability for ±2σ range (from 12 to 28 in this case).
Let me know if you'd like a visual graph showing this distribution as well!