Question

Marina has learned that it typically rains 43% of the days in August in the city where she lives.

Assuming that the probability of rain on each day is independent, find the variance in the number of rainy days in Marina's city in two weeks during the month of August.

Answer 1

To find the variance in the number of rainy days in Marina's city in two weeks during the month of August, calculate the mean and standard deviation. The mean number of rainy days is 6.02, and the standard deviation is 1.78. Therefore, the variance is 3.17.

Step-by-step explanation:

To find the variance in the number of rainy days in Marina's city in two weeks during the month of August, we need to first calculate the mean and standard deviation.

The mean number of rainy days in August is 43% of the total number of days, so for a two-week period, there would be 14 * 0.43 = 6.02 rainy days on average.

The standard deviation can be calculated using the formula:

Standard Deviation = sqrt(n * p * (1 - p))

Where n is the number of trials (14 days) and p is the probability of success (0.43).

Plugging in the values, we get:

Standard Deviation = sqrt(14 * 0.43 * (1 - 0.43)) = 1.78

The variance can be calculated by squaring the standard deviation:

Variance = (Standard Deviation)^2 = 1.78^2 = 3.17

So, the variance in the number of rainy days in Marina's city in two weeks during the month of August is 3.17.