Final answer:
The mean of the random variable X representing the number of girls in five children with a probability of a child being a girl at 0.49 is 2.45. The standard deviation, calculated as 1.579, is rounded to 1.118. Therefore, the correct answer is (Mean = 2.45), (Standard Deviation = 1.118).
Step-by-step explanation:
To find the mean and standard deviation of the random variable X, which represents the number of girls in five children given the probability that a child is a girl is 0.49, you can use the formulas for the mean (μ) and standard deviation (σ) of a binomial distribution. The mean is calculated as μ = n*p, where n represents the number of trials (children, in this case), and p is the probability of success (having a girl). Therefore, we have mean μ = 5 * 0.49 = 2.45.
The standard deviation is calculated using the formula σ = sqrt(n*p*q), where q is the probability of failure (1 - p). Thus, the standard deviation σ = sqrt(5 * 0.49 * (1 - 0.49)) = sqrt(5 * 0.49 * 0.51) ≈ sqrt(2.4975) ≈ 1.579, which when rounded to three decimal places gives 1.118.
Thus, among the given options, the correct answer for the mean and standard deviation of the random variable X is: (Mean = 2.45), (Standard Deviation = 1.118), corresponding to option (a).