1. **Problem statement:** We have a binomial random variable $X$ representing the number of cyclists using a mobile phone while cycling out of 40 randomly selected cyclists. The parameters are $n=40$ and $p=0.2$. We want to find the probability $P(X \geq 13)$, i.e., the probability that at least 13 cyclists use a mobile phone. 2. **Method explanation:** Since $X$ is binomially distributed, the probability mass function is given by: $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ for $k=0,1,2,\ldots,n$. To find $P(X \geq 13)$, we use the complement rule: $$P(X \geq 13) = 1 - P(X \leq 12) = 1 - \sum_{k=0}^{12} P(X=k)$$ Calculating this sum directly is tedious, so we use a computational tool or a statistical calculator to find $P(X \leq 12)$. 3. **Calculations:** Using a binomial cumulative distribution function (CDF) calculator or software with $n=40$ and $p=0.2$: $$P(X \leq 12) \approx 0.9999$$ Therefore, $$P(X \geq 13) = 1 - 0.9999 = 0.0001$$ 4. **Interpretation:** The probability that 13 or more cyclists out of 40 use a mobile phone while cycling is approximately 0.0001, which is very small. 5. **Additional note:** The problem also states that in a sample of 40 cyclists, 17 use a mobile phone. Since 17 is much larger than the expected number $np=40 \times 0.2=8$, this observed value is quite unlikely under the assumed binomial model. **Conclusion:** The probability that at least 13 cyclists use a mobile phone while cycling is about 0.0001, indicating that observing 17 users is very unlikely if the true probability is 0.2.