Indigo Electronics manufactures electric circuit breakers. When trying to determine how long they take to manufacture each circuit breaker, they took $10$ observations of units being produced as a sample. The results were as follows:

$1)10$ minutes

$2)12$ minutes

$3)8$ minutes

$4)8$ minutes

$5)15$ minutes

$6)11$ minutes

$7)9$ minutes

$8)11$ minutes

$9)14$ minutes

$10)8$ minutes

$5\mathrm{.}1)$ Indigo Electronics has quoted a customer based on a costing of $10$ minutes to manufacture an electric circuit breaker. Assuming that we are considering downside risk, calculate with a $95\%$ confidence level how long it will take to manufacture each circuit breaker. To do this calculation, you will have to determine the mean and the standard deviation for the distribution. Please show or explain how you reach your answer. $($Max$.15$ lines$)$

$5\mathrm{.}2$ Based on your findings, at a $95\%$ confidence level, do you think that Indigo Electronics has allowed sufficient manufacturing time compared to its initial costing of $10$ minutes per unit? If not, please explain what the result of this could be$.($Max$.4$ lines$)$