I see that you've uploaded an image with a set of questions regarding a probability model for people entering a security check-in lineup at an airport. Let's go through the problem step by step.

Part (a)

The model you provided is a Poisson distribution given by:

$P(X = x) = \frac{e^{-19.2}(19.2)^x}{x!}, \quad x = 0, 1, 2, \dots$

In this model, the parameter 19.2 is the mean or average number of people entering the security lineup in a 15-minute interval.

The correct interpretation of 19.2 in this context is B. 19.2 represents the average number of people who enter a security check-in lineup every 15 minutes.

Part (b)

For Part (b), you are asked to compute the probability that exactly 17 people enter the security check-in lineup in a 15-minute interval.

The probability mass function for a Poisson distribution is:

$P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!}$

Here, $\lambda = 19.2$ and $x = 17$. Plug these values into the formula to compute $P(X = 17)$:

$P(X = 17) = \frac{e^{-19.2}(19.2)^{17}}{17!}$

You can now compute this value using a calculator or a software tool.

Part (c)

For Part (c), you are asked to compute the probability that at least 5 people will enter the security check-in lineup in a 5-minute interval.

To solve this, we need to scale the Poisson distribution since the time interval is now 5 minutes. The rate parameter for 5 minutes would be:

$\lambda_{\text{5 min}} = \frac{19.2}{3} = 6.4$

Now, you need to compute the probability that at least 5 people enter the security lineup in 5 minutes, which is:

$P(X \geq 5) = 1 - P(X < 5)$

This can be computed using the Poisson cumulative distribution function for $X = 0, 1, 2, 3, 4$ with $\lambda = 6.4$, then subtracting from 1.

Part (d)

In Part (d), you are told that between 13 and 20 people (inclusive) have entered the lineup, and you are asked to compute the probability that this number is exactly 17.

To solve this, you can compute:

$P(13 \leq X \leq 20) = P(X = 13) + P(X = 14) + \dots + P(X = 20)$

Each of these can be computed using the Poisson distribution with $\lambda = 19.2$.

Would you like me to compute the exact values for any of these parts or guide you on how to do it step-by-step?