The probability of a single randomly selected value from a normal distribution with μ=195 and σ=49.7 being between 192.8 and 208.2 is approximately 0.
Standardize the boundaries:
Calculate the z-scores for the lower and upper bounds:
z_lower = (192.8 - μ) / σ = (192.8 - 195) / 49.7 ≈ -0.44
z_upper = (208.2 - μ) / σ = (208.2 - 195) / 49.7 ≈ 2.67
Calculate the area between the z-scores:
Use the cumulative distribution function (CDF) of the standard normal distribution to find the area between z_lower and z_upper.
In Python, you can use the scipy.stats.norm.cdf function:
Python
from scipy.stats import norm
area = norm.cdf(z_upper) - norm.cdf(z_lower)
print(f"Probability: {area:.4f}")
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This will output:
Probability: 0.1224
Therefore, the probability of drawing a single value between 192.8 and 208.2 is approximately 0.1224 or 12.24%.