UNIFORM DISTRIBUTION . Suppose X is a continuous random variable whose pdf is a at line between two values a and b. In dais case we say that X has a uniform distribution over the interval [a, b]. For any X values outside the range , f(x) is zero . NOTE : ALWAYS DRAW PICTURES WHEN SOLVING PROBLEMS LIKE THE ONES BELOWo IT WILL HELP YOU AND WE'LL BE EXPECTING TO SEE THEM. For the next 5 problems: Suppose a manager of a phone helpline wants to limit the time a customer has to wait on hold to less than 10 minutes .Assuming this actually happens , let X be the amount of time a customer is on hold . Assume X has a uniform distribution over the interval [0, 10]. 3. Graph f{x). 4. Find the probability that a customer waits less than 2 minutes using integration 5- Suppose the manager's goal is for the customers to wait no longer than 2.5 minutes .What percentage of the time is her goal being met under the current situation . For the next 5 problems: A company making candles guarantees their candles will last at least 2 hours , just to be safe . Prior research done by the company shows the candles can actually last from 2 up to 12 hours .Let X represent the lifetime of a candle made by this company . Assume X has a uniform distribution over [2, 12]. 6. Find and graph f(x). Remember the possible values of X start at 2, not zero . 7. Find the probability that a candle lasts between 10 and 12 hours . 8. Find the probability that a candle lasts more than 8 hours . 9. Find median wait time using integration .Use the following hint : The median is the value of X where 50% of the area lies below X. This means you know the integral is equal to .50 and your job is to find the upper limit of the integral. You know the lower limit is 2. 10. Using the same procedure as above , find the wait time that marks the 25 th percentile (in other words , find Q1.) 11. Suppose X has a uniform distribution over [0, 4]. Find f(x)