The rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. suppose the rockwell hardness of a particular alloy is normally distributed with mean 68 and standard deviation 3. (a) if a specimen is acceptable only if its hardness is between 65 and 71, what is the probability that a randomly chosen specimen has an acceptable hardness? (round your answer to four decimal places.) 0.6826 correct: your answer is correct.

0.6826

Step-by-step explanation:

Since it's a normal distribution

z = (x - m)/s where

m = mean = 68

s = standard deviation = 3

z = standard normal variable

x = values of hardness of the specimen

a) we are looking for P( 65 lesser than/equal to x lesser than/ equal to 71

For x= 65,

z = (65-68)/3 = -3/3 = -1

For x= 71

z = (71 -68)/3 = 3/3 =1

Looking at the normal distribution table,

For area covered by

(z = -1 to z= 1) = 0.1587

For area covered by

(z = 0 to z=1) = 0.8413

P( 65 lesser than/equal to x lesser than/ equal to 71) = 0.8413 -0.1587

= 0.6826

the 1st digit is in the 100s n its 1

step-by-step explanation:

3,589÷18 = 199.389

so the first digit of the quotient is in the 100s n its 1

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true