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

45

step-by-step explanation:

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following