Find the area under the standard normal probability distribution between the following pairs of z-scores. a. zequals0 and zequals1.00 e. zequalsminus1.00 and zequals0 b. zequals0 and zequals2.00 f. zequalsminus2.00 and zequals0 c. zequals0 and zequals3.00 g. zequalsnegative 1.49 and zequals0 d. zequals0 and zequals0.82 h. zequalsminus0.82 and zequals0

See below

Step-by-step explanation:

All this values can be easily found by using a table or a spreadsheet.

a)

P(0 ≤ z ≤ 1) = 0.3413

e)

P(-1 ≤ z ≤ 0) = P(0 ≤ z ≤ 1) = 0.3413 because N(0;1) is symmetrical

b)

P(0 ≤ z ≤ 2) = 0.4772

f)

P(-2 ≤ z ≤ 0) = P(0 ≤ z ≤ 2) = 0.4772

c)

P(0 ≤ z ≤ 3) = 0.4987

g)

P(-1.49 ≤ z ≤ 0) = 0.4319

d)

P(0 ≤ z ≤ 0.82) = 0.2939

h)

P(-0.82 ≤ z ≤ 0) = P(0 ≤ z ≤ 0.82) = 0.2939

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form