Scores on a english test have average of 85 with standard deviation of 8. what is the probabilty of a student scoring less than 77 on the test? write your answer as a percent.

47.725%

If the mean (μ) is 80, and the standard deviation (σ) is 5, then all scores between 80 and 90 would fall between 0 and 2 standard deviations above the mean.

Using the equation for Z score (Z = (X-μ)/σ) for each X value (80 and 90) then the Z scores are 0 and 2, respectively.  

Using a normal distribution table, it can be found that P(80 < z) = .5 (this is the probability that a random score would be greater than 80.  It makes sense that it is .5 or 50% because 80 is the mean.)

And the P(90 > z) = .97725.  (this is the probability that a random score would be less than 90.)

10

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: