Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from cincinnati to tampa. suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. what is the probability that the flight will be no more than 5 minutes late?

 0.5

Step-by-step explanation:

Given : Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa.

i.e. Flight time =   2(60) +5= 125 minutes  [∵ 1 hour = 60 minutes]

Actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.

i.e. In minutes the flight times are between 120 minutes and 140 minutes.

Let x be a uniformly distributed variable in [120 minutes, 140 minutes] that  represents the flight time.

Since the probability density function for x uniformly distributed in [a,b] is

⇒ Probability density function for flight time  :

5 minutes late than usual time = Flight time+ 5 = 125+5 = 130 minutes

Now , the probability that the flight will be no more than 5 minutes late will be :-

Hence, the probability that the flight will be no more than 5 minutes late is 0.5.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: