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Answer :
Final answer:
The variance of the number of days Pete will catch fish, denoted as X, is approximately 0.38 when rounded to two decimal places. Therefore the correct answer is a.
Explanation:
Since the probability that Pete will catch a fish on any given day is 0.85, we are dealing with a binomial distribution. For a binomial distribution, the variance is given by the formula variance = np(1-p), where 'n' is the number of trials, 'p' is the probability of success on each trial, and '1-p' is the probability of failure.
Here, the number of trials (days) 'n' is 3, and the probability of success 'p' is 0.85. We can calculate the variance as follows:
Variance = n × p × (1 - p)
Variance = 3 × 0.85 × (1 - 0.85)
Variance = 3 × 0.85 × 0.15
Variance = 3 × 0.1275 = 0.3825
Once calculated, we find that the variance of X is approximately 0.38 when rounded to two decimal places.
Variance is a measure of the spread or dispersion of a set of data points around their mean. It quantifies how much the values in a dataset differ from the mean value. The sample variance formula divides by −1n−1 instead of n to correct for bias in the estimation of population variance. This correction accounts for the fact that the sample mean is used to estimate the population mean.
Variance is an important measure in statistics and data analysis, providing insights into the variability and distribution of data points in a dataset. It is commonly used in conjunction with other statistical measures, such as the standard deviation, to characterize the spread of data and make comparisons between datasets.
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