Examkin

Question

Difficulty: MediumExperimental 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.

Answer: 5 days

Answer

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.

Step-by-Step Solution

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).

Key Concept

Difference Between Experimental Frequency and Theoretical Expectation
Rate this question

Topics

Experimental and Theoretical Probability

More questions from this topic