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 if 53 ≤ x ≤ 57, otherwise You may assume that the production times for producing different blenders are independent of each other. 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. c. 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%? Answer question 3

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I use TI-nspire cx I do not know what or how to write this to calculator to find out the median and mode
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.
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.
c.
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%?
Answer question 3
Transcribed Image Text: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. 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. c. 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%? Answer question 3
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