Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.4 millimeters (mm) and a standard deviation of 0.8 mm. For a randomly found shard, find the following probabilities. a. the thickness is less than 3.0 mm
b. the thickness is more than 7.0 mm
c. the thickness is between 3.0 mm and 7.0 mm

a) the required probability is 0.0013

b) the required probability is 0.0288

c) the required probability is 0.9759

Step-by-step explanation:

Given the data in the question;

let x be the thickness measurements

Given that X follows a Normal distribution with mean μ = 5.4

standard deviation σ = 0.8

then z = x-μ / σ = x-5.4 / 0.8   follows standard Normal

a) probability that the thickness is less than 3.0 mm

P( x<3 ) = P( x-5.4 / 0.8  <  3-5.4 / 0.8 ) = P( Z < -3.00 ) = 0.0013

Therefore, the required probability is 0.0013

b) the thickness is more than 7.0 mm

P( x>7 ) = P( x-5.4 / 0.8  >  7-5.4 / 0.8 ) = P( Z > 2.00)

= 1 - P( Z ≤ 2)

= 1 - 0.9772

= 0.0288

Therefore, the required probability is 0.0288

c) the thickness is between 3.0 mm and 7.0 mm

P(3< x<7 ) = P( x<7) - P(x<3)

= P( x-5.4 / 0.8  >  7-5.4 / 0.8 )  - P( x-5.4 / 0.8  <  3-5.4 / 0.8 )

= P( Z< 2 ) - P( Z < -3)

= 0.9772 - 0.0013

= 0.9759

Therefore, the required probability is 0.9759

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

none of these

step-by-step explanation:

23 + 34 add up to 57 so just inform the teacher of this really stupid mistake