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Zorluk: OrtaExperimental and Theoretical Probability

In a meteorological study conducted over 120120 days in a coastal town, rain was observed on 4545 days. According to a theoretical weather model, the probability of rain on any given day during this period is 13\frac{1}{3}. Calculate the absolute difference between the observed number of rainy days and the expected number of rainy days predicted by the theoretical model.

Cevap: 5 days

Cevap

The absolute difference between the observed and expected number of rainy days is 5 days.
The expected number of rainy days based on theoretical probability is 13×120=40\frac{1}{3} \times 120 = 40 days. The experimental observation recorded 4545 rainy days. The absolute difference between the observed and expected number of rainy days is ∣45−40∣=5|45 - 40| = 5 days.

Adım Adım Çözüm

1
Calculate the theoretical expected number of rainy days
Expected rainy days = 40
Multiply the total number of trial days (120) by the theoretical probability of rain (1/3).
2
Identify the experimental (observed) number of rainy days
Observed rainy days = 45
The problem states that rain occurred on 45 days during the 120-day period.
3
Compute the positive absolute difference
Absolute difference = 5
Subtract the theoretical expected count (40) from the experimental observed count (45).

Anahtar Kavram

Difference Between Experimental Frequency and Theoretical Expectation
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Konular

Experimental and Theoretical Probability

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