Assume that when adults with smartphones are randomly selected, \( 54 \% \) use them in meetings or classes. If 20 adult smartphone users are randomly selected, find the probability that exactly 13 of them use their smartphones in meetings or classes. The probability is \( \square \). (Round to four decimal places as needed.)

To find the probability that exactly 13 out of 20 adult smartphone users use them in meetings or classes, we can use the binomial probability formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n \) is the total number of trials (20), - \( k \) is the number of successful trials (13), - \( p \) is the probability of success (0.54), - \( \binom{n}{k} \) is the binomial coefficient. Now let’s calculate it step-by-step: 1. Calculate the binomial coefficient \( \binom{20}{13} \): \[ \binom{20}{13} = \frac{20!}{13!(20-13)!} = \frac{20!}{13!7!} = 77520 \] 2. Calculate \( p^k \) and \( (1-p)^{n-k} \): \[ p^k = (0.54)^{13} \approx 0.005845 \] \[ (1-p)^{n-k} = (0.46)^{7} \approx 0.006737 \] 3. Now plug these values into the binomial probability formula: \[ P(X = 13) = 77520 \times (0.54)^{13} \times (0.46)^{7} \] \[ P(X = 13) \approx 77520 \times 0.005845 \times 0.006737 \approx 0.03945 \] Therefore, rounding to four decimal places, the probability is \( 0.0395 \).