A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is: a. 0.9545.
b. 0.9332.
c. 0.0668.
d. 0.4332.

0.9545

Step-by-step explanation:

Given that :

Mean = 300

Standard deviation, σ = 18

Sample size, n = 144

Zscore = (x - mean) ÷ σ/√n

At score, x = 297

Zscore = (297 - 300) / (18/12) = - 2

P(Z< - 2) = 0.02275

At score, x = 303

Zscore = (303 - 300) / (18/12) = 2

P(Z< 2) = 0.97725

P(Z < 2) - P(Z < - 2) = 0.97725 - 0.02275 = 0.9545

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1