The average life of a certain type of small motor is 8 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under warranty. If she is willing to provide a 5-year and the distribution of the motor lives is normal, calculate the percentage of motors that will have to be replaced. Use 3 decimal places and enter your answer as a decimal value

And we can find this probability using the normal standard distribution or Excel:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the average life of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

Since all the motors with an average life of lesss than 5 years satisfy the warranty period

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the normal standard distribution or Excel:

$35.59 in pounds

step-by-step explanation:

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: