This is a pretty simple calculator. mu here is the mean of the random variable and sigma is one standard deviation from the mean. You're on the job doing what people do and you have to calculate the probability of a successes around the mean and within a parameter that we define here as lower_bound and upper_bound.
This code in Python.
Made simple so you know what you're dealing with.
The result should be:
The percentage of scores between 808 and 1450 is approximately 88.14%.
# Set the parameters
mu = 1359
sigma = 77
lower_bound = 808
upper_bound = 1450
# Calculate the z-scores for the lower and upper bounds
z_lower = (lower_bound - mu) / sigma
z_upper = (upper_bound - mu) / sigma
# Calculate the probabilities using the cumulative distribution function (CDF)
prob_lower = norm.cdf(z_lower)
prob_upper = norm.cdf(z_upper)
# Calculate the percentage between the bounds
percentage = (prob_upper - prob_lower) * 100
print(f"The percentage of scores between {lower_bound} and {upper_bound} is approximately {percentage:.2f}%.")
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