The lengths of a professor's classes has a continuous uniform distribution between 49.2 min and 55.5 min. If one such class is randomly selected, find the probability that the class length is more than 53.1 min. PX < 53.1)

And

Step-by-step explanation:

Let X the random variable who represent the  lengths of a professor's classes and we know that the distribution for X is given by:

And for this case we want to find the following probability:

We can use the cumulative distribution function given by:

And if we use this formula and the complement rule we got :

And

something over 10 so ? /10

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.