Challenge: Solving Task Using Gaussian Distribution
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Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.
Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.
You have to:
- Calculate the probability that pressure is in the
[740, 760]range. - Calculate the probability that pressure is in the
[750, 770]range. - As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.
Solução
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from scipy.stats import norm
mean = 760
std_dev = 15
# Calculate the probability of pressure between 740 and 760
prob_range_1 = norm.cdf(760, mean, std_dev) - norm.cdf(740, mean, std_dev)
# Calculate the probability of pressure between 750 and 770
prob_range_2 = norm.cdf(770, mean, std_dev) - norm.cdf(750, mean, std_dev)
# Calculate the probability of pressure in both ranges
prob_intersection = norm.cdf(760, mean, std_dev) - norm.cdf(750, mean, std_dev)
# Calculate the combined probability using the inclusion-exclusion principle
combined_prob = prob_range_1 + prob_range_2 - prob_intersection
print(f'Probability is {combined_prob:.4f}')
Tudo estava claro?
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Seção 4. Capítulo 5
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from scipy.stats import norm
# Parameters of the distribution
mean = 760
std_dev = 15
# Calculate the probability of pressure between 740 and 760
prob_range_1 = norm.___(___, mean, std_dev) - norm.___(___, mean, std_dev)
# Calculate the probability of pressure between 750 and 770
prob_range_2 = norm.___(___, mean, std_dev) - norm.___(___, mean, std_dev)
# Calculate the probability of pressure in both ranges
prob_intersection = norm.cdf(___, mean, std_dev) - norm.cdf(___, mean, std_dev)
# Calculate the combined probability using the inclusion-exclusion principle
combined_prob = prob_range_1 + prob_range_2 - prob_intersection
print(f'Probability is {combined_prob:.4f}')
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