The proportion of TikTok users ages \( 40-49 \) is estimated to be \( 20.3 \% \). In a randomly selected sample of 147 TikTok users, find the probability that you observe \( 20 \% \) or less users aged \( 40-49 \). You may use the Normal Distribution tool. Mean should not be rounded, standard deviation may be rounded to four decimal places. Round proportions to four decimal places or percentages to two decimal places. If entering a percentage, include the \% symbol.

To find the probability that you observe \(20\%\) or less users aged \(40-49\) in a sample of \(147\) TikTok users, we'll use the normal approximation to the binomial distribution. First, we need to determine the mean and standard deviation for the binomial distribution. 1. **Calculate the Mean (\(\mu\))**: \[ \mu = n \cdot p = 147 \cdot 0.203 = 29.901 \] 2. **Calculate the Standard Deviation (\(\sigma\))**: \[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} = \sqrt{147 \cdot 0.203 \cdot (1 - 0.203)} \\ = \sqrt{147 \cdot 0.203 \cdot 0.797} \\ = \sqrt{23.4877} \approx 4.8433 \] 3. **Convert the proportion of users (20%) to the number of users**: \[ X = 0.20 \cdot 147 = 29.4 \] Since we can't have a fraction of a user, we consider \(X \leq 29\) (which is the closest whole number). 4. **Standardize (convert to a Z-score)**: \[ Z = \frac{X - \mu}{\sigma} = \frac{29 - 29.901}{4.8433} \approx \frac{-0.901}{4.8433} \approx -0.1866 \] 5. **Find the Probability**: Now we will look up the Z-score of \(-0.1866\) in the standard normal distribution table or use a calculator. The probability corresponding to a Z-score of \(-0.1866\) is approximately \(0.4266\) (or \(42.66\%\)). Therefore, the probability that you observe \(20\%\) or less users aged \(40-49\) in a randomly selected sample of \(147\) TikTok users is approximately **42.66%**.