A plant manufacturers part whose lengths are normally distributed with a mean of 16.3 centimeters and a standard deviation of 2.5 centimeters. 20% of all parts are below what length?

20% of all parts are below 14.2 cm

Step-by-step explanation:

The formula of the z score is z = (x - μ)/σ, where μ is the mean, σ is the standard deviation

∵ P(x < h) = 20%

∵ 20% = (20/100) = 0.2

∴ P(x < h) = 0.2

Let us use the normal distribution table to find z-score of the corresponding area 0.2

∵ z-score of the corresponding area 0.2 is - 0.845

∵ The mean is 16.3 cm

∴ μ = 16.3

∵ The standard deviation is 2.5 cm

∴ σ = 2.5

- Substitute these values in the formula above to find h

∵ -0.845 = (h - 16.3)/2.5

- Multiply both sides by 2.5

∴ - 2.1125 = h - 16.3

- Add 16.3 to both sides

∴ 14.1875 = h

- Round it to the nearest tenth

∴ h = 14.2 cm

20% of all parts are below 14.2 cm

{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

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.