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.

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UpStudy AI · Accepted Answer

The sampling distribution of the sample proportion has a mean given by

$$
\mu = p
$$

and a standard deviation given by

$$
\sigma = \sqrt{\frac{p(1-p)}{n}}.
$$

Given $$ p = 0.045 $$ and $$ n = 375 $$, we can calculate as follows:

**(a) Mean:**

$$
\mu = 0.045.
$$

**(b) Standard Deviation:**

1. First, calculate $$ p(1-p) $$:

$$
p(1-p) = 0.045 \times (1 - 0.045) = 0.045 \times 0.955 = 0.042975.
$$

2. Next, divide by $$ n $$:

$$
\frac{0.042975}{375} \approx 0.0001146.
$$

3. Finally, take the square root:

$$
\sigma = \sqrt{0.0001146} \approx 0.0107.
$$

Thus, the answers are:

$$
\text{(a) Mean} = 0.045,
$$
$$
\text{(b) Standard Deviation} = 0.0107.
$$
**(a) Mean:** 0.045 **(b) Standard Deviation:** 0.0107

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