The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = { 0.075x + 0.2 3 ≤ x ≤ 5 0 otherwise Calculate P(3.5 ≤ X ≤ 4.5)

please do this typewritten asap.

Moulinex is a well-known brand on the market that produces blenders. The time needed to produce one blender is expressed in minutes and can be modelled as a continuous random variable X with density function f(x) = {a ·⋅ (x − 53) · (57 − x)³ 0 if 53 ≤ x ≤ 57, otherwise You may assume that the production times for producing different blenders are independent of each other. C. a. Show that a = 1 / 51.2. b. Determine the median production time and the mode of the production time of the blenders of the brand Moulinex. Determine the probability that the total production time needed to produce 50 blenders exceeds 45 hours. d. What is the maximum number of blenders that can be produced with a total production time of at most 40 hours with a probability of at least 95%?