6.3 The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable X having a continuous uniform distribution with A = 7 and B = 10. Find the probability that on a given day the amount of coffee dispensed by this machine will be (a) at most 8.8 liters; (b) more than 7.4 liters but less than 9.5 liters; (c) at least 8.5 liters.

a) 60% probability that on a given day the amount of coffee dispensed by this machine will be at most 8.8 liters.

b) 70% probability that on a given day the amount of coffee dispensed by this machine will be more than 7.4 liters but less than 9.5 liters

c) 50% probability that on a given day the amount of coffee dispensed by this machine will be at least 8.5 liters

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

The probability of X being higher than x is:

The probability of X being between c and d is:

For this problem, we have that:

(a) at most 8.8 liters;

60% probability that on a given day the amount of coffee dispensed by this machine will be at most 8.8 liters.

(b) more than 7.4 liters but less than 9.5 liters;

70% probability that on a given day the amount of coffee dispensed by this machine will be more than 7.4 liters but less than 9.5 liters

(c) at least 8.5 liters.

50% probability that on a given day the amount of coffee dispensed by this machine will be at least 8.5 liters

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b