Question

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X= the number of American adults out of a random sample of 50 who prefer saving to spending. What is the mean (μ) and standard deviation (σ) of X? Select the correct answer below: μ=12 and σ≈3.46 μ=12 and σ≈4.47 μ=12 and σ≈5.48 μ=30 and σ≈3.46 μ=30 and σ≈4.47 μ=30 and σ≈5.48

Answer 1

The mean (μ) and standard deviation (σ) of X, where X is the number of American adults out of a sample of 50 who prefer saving to spending and 60% prefer saving, are calculated as μ=30 and σ≈3.46.

Step-by-step explanation:

To calculate the mean (μ) and standard deviation (σ) of X, where X is the number of American adults out of a random sample of 50 who prefer saving to spending and 60% prefer saving, we use the formulas for the mean and standard deviation of a binomial distribution:

• Mean (μ) = np
• Standard deviation (σ) = sqrt(np(1 - p))

Where 'n' is the sample size and 'p' is the probability of preferring saving. In this case, n = 50 and p = 0.60:

• μ = 50 * 0.60 = 30
• σ = sqrt(50 * 0.60 * (1 - 0.60))
• σ = sqrt(50 * 0.60 * 0.40) = sqrt(12) ≈ 3.46

Therefore, the correct answer is μ=30 and σ≈3.46.