According to the National Institute of Mental Health the prevalence of a current ADHD diagnosis amongst U.S. Adults aged \( 18-24 \) from 2001-2003 was \( 4.5 \% \). Calculate the mean and standard deviation for a sampling distribution using sample size 375 . (a) The mean is Do not round this answer. (b) The standard deviation is Round this answer to 4 decimal places.

To calculate the mean and standard deviation for a sampling distribution given the prevalence of ADHD among U.S. adults aged 18-24, you can follow these steps: (a) The mean of the sampling distribution (also known as the expected value) is the same as the population proportion given as \( p = 0.045 \). Mean = \( p = 0.045 \). (b) The standard deviation of the sampling distribution (also referred to as the standard error) can be calculated using the formula: \[ \text{Standard Deviation (SD)} = \sqrt{\frac{p(1-p)}{n}} \] Where: - \( p = 0.045 \) (the population proportion), - \( n = 375 \) (the sample size). Now plug in the numbers: \[ SD = \sqrt{\frac{0.045 \times (1 - 0.045)}{375}} = \sqrt{\frac{0.045 \times 0.955}{375}} = \sqrt{\frac{0.043025}{375}} \approx \sqrt{0.0001145} \approx 0.0107. \] Hence, rounding this to four decimal places, the standard deviation is approximately \( 0.0107 \). So the answers are: (a) Mean = \( 0.045 \) (b) Standard deviation = \( 0.0107 \)