What interval contains approximately two-thirds of the weights, given a normal distribution with mean 150 lb and standard deviation 10 lb?

For a normal distribution, the Empirical Rule (or 68-95-99.7 rule) states that approximately 68% of the data falls within one standard deviation (±1 SD) of the mean. "Two-thirds" is approximately 66.7%, which is closest to 68%. Therefore, we need to find the interval within ±1 standard deviation from the mean.

• Mean (μ) = 150 lb
• Standard Deviation (σ) = 10 lb

The interval is given by: (μ - 1σ) to (μ + 1σ)

• Lower bound = 150 lb - (1 × 10 lb) Lower bound = 150 lb - 10 lb Lower bound = 140 lb

• Upper bound = 150 lb + (1 × 10 lb) Upper bound = 150 lb + 10 lb Upper bound = 160 lb

The interval that includes approximately two-thirds of all weights is 140-160 lb.

Comparing this to the given options:

a) 145-155

b) 140-160

c) 130-170

d) 130-150

e) 150-170

The correct option is b) 140-160 lb.