Background: You are a project manager at a software company working on a new product feature. Based on historical data, you know that the time to complete similar tasks can vary widely due to unforeseen issues, changes in requirements, and varying developer productivity. To manage expectations and plan for contingencies, you decide to use a Monte Carlo simulation to estimate the probability that the project will be completed within the deadline.

Scenario: The new feature development is broken down into $4$ key tasks. The completion time for each task $($in days$)$ is random and follows a specific probability distribution based on expert estimates and historical data:

Task $1$: Normally distributed with a mean of $10$ days and a standard deviation of $2$ days.

Task $2$: Uniformly distributed between $5$ and $15$ days.

Task $3$: Normally distributed with a mean of $8$ days and a standard deviation of $3$ days.

Task $4$: Uniformly distributed between $7$ and $12$ days.

The deadline for the project is $40$ days from now.

Q$5\mathrm{.}1$ What is the probability of completing the project within the deadline? $(7$ Points$)$

Write a Monte Carlo Simulation using NumPy to estimate the probability of completing the project within the deadline. Assume that the tasks are completed sequentially. You will perform at least $10,000,000$ trials.