Question

1. Suppose the mean weight of infants born in a community is µ= 3380 g and σ= 500 g

   1. What proportion will be between 2000 and 4000 grams?

   2. What proportion will be between 3000 and 3350 grams?

   3. What proportion will be between 3400 and 3800 grams?

   4. What proportion will be less than 2380 grams?

Answer 1

1. What proportion will be between 2000 and 4000 grams?

z = (x - µ)/σ = (2000 - 3380)/500 = -2.76

P(z = -2.76) = 0.0029

​​​​​​​z = (x - µ)/σ = (4000 - 3380)/500 = 1.24

P(z = 1.24) = 0.8925

Required proportion = 0.8925 - 0.0029 = 0.8896

1. What proportion will be between 3000 and 3350 grams?

​​​​​​​​​​​​​​z = (x - µ)/σ = (3000 - 3380)/500 = -0.76

P(z = -0.76) = 0.2236

​​​​​​​z = (x - µ)/σ = (3350 - 3380)/500 = -0.06

P(z = -0.06) = 0.4761

Required proportion = 0.4761 - 0.2236 = 0.2525

1. What proportion will be between 3400 and 3800 grams?

​​​​​​​​​​​​​​​​​​​​​z = (x - µ)/σ = (3400 - 3380)/500 = 0.04

P(z = 0.04) = 0.5160

​​​​​​​z = (x - µ)/σ = (3800 - 3380)/500 = 0.84

P(z = 0.84) = 0.7995

Required proportion = 0.7995 - 0.5160 = 0.2836

1. What proportion will be less than 2380 grams?

​​​​​​​​​​​​​​​​​​​​​​​​​​​​z = (x - µ)/σ = (2380 - 3380)/500 = -2

P(z < -2) = 0.0228

Please give me a thumbs-up if this helps you out. Thank you!