$4\mathrm{.}3[2$ pt$]$ Suppose that, instead of observing the decision of one of its customers about whether or not to purchase the product, it observes the decisions of $100$ of its customers. Again, the price is $$4\mathrm{.}25,$ the standard deviation is $$0\mathrm{.}37,$ the initial probability that the mean of the customers' valuations is $$3\mathrm{.}95$ is $40\%,$ and the initial probability that the mean of the customers' valuations is $$4\mathrm{.}05$ is $60\%.$ Write a function called prob$\_395$ that takes as its input a list of $100$ integers $($ones and zeros$)$ where a $1$ means the customer purchased the product and a $0$ means that he did not. It should return the updated probability that the mean of the customers' valuations is $$3\mathrm{.}95.$

In $[20]$:

Student's answer

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def prob$\_395($purchase$\_$decisions$)$: