Answer:
20% of all parts are below 14.2 cm
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