Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company. suppose that a normal distribution with mean μ = 5 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. use the normal distribution model to calculate the probabilities below. (round all answers to four decimal places.)

(a) p(x > 5) =
(b) p(x < 5.4)=

(c) p(x lteq. gif 5.4) =

(d) p(4.6 < x < 5.2) =

(e) p(x > 4.5) =

(f) p(x > 4) =

A) 0.5000; B) 0.9772; C) 0.9772; D) 0.8185; E) 0.9932; F) 1.0000

Step-by-step explanation:

For each of these, we will use a z score.  The formula for a z score is:

A) Our X is 5, our mean is 5 and our standard deviation is 0.2:

z = (5-5)/(0.2) = 0/0.2 = 0

Using a z table, the value to the left of this, less than, is 0.5000; this means the area to the right of this, greater than, is 1-0.5000 = 0.5000.

B) Our X is 5.4, the mean is 5 and the standard deviation is 0.2:

z = (5.4-5)/0.2 = 0.4/0.2 = 2

Using a z table, the value to the left of this, less than, is 0.9772.

C) The probability for this will be the same as for B; there is no distinction between "less than" and "less than or equal to" in z tables.

D) We find the z score for each of the endpoints of this interval, find the probabilities and subtract them:

z = (4.6-5)/0.2 = -0.4/0.2 = -2; the probability is 0.0228.

z = (5.2-5)/0.2 = 0.2/0.2 = 1; the probability is 0.8413.

The area between them is 0.8413-0.0228 = 0.8185.

E) X is 4.5, the mean is 5 and the standard deviation is 0.2:

z = (4.5-5)/0.2 = -0.5/0.2 = -2.5; the probability less than this is 0.0062.  This means the probability greater than this is 1-0.0062 = 0.9938.

F) X is 4, the mean is 5 and the standard deviation is 0.2:

z = (4-5)/0.2 = -1/0.2 = -5.  Everything in the z table is larger than this, so the probability is 1.000.

answer: 370

step-by-step explanation:

remember use pemdas! there are no parentheses or exponents so lets move onto the first part of the equation: multiplication and division. first, lets break the first part of the equation up into something easier using the distributive property. 28 * 12= (20 *12) + (8*12) you know that 20*12 is 240 and 8*12 is 96. add them and you get 336. then, lets solve the last part of the equation (the last part of pemdas is addition and subtraction). 336 plus 34 is 370. hope this !

i believe the answer is the polygon, heptagon.