Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams. Assume that birth weight data are approximately bell-shaped. Part 1 of 3 (a) Estimate the number of newborns whose weight was less than 4171 grams. Approximately of the 732 newborns weighed less than 4171 grams. Part 2 of 3 (b) Estimate the number of newborns whose weight was greater than 1591 grams. Approximately of the 732 newborns weighed more than 1591 grams. Part 3 of 3 (c) Estimate the number of newborns whose weight was between 3311 and 5031 grams. Approximately of the 732 newborns weighed between 3311 and 5031 grams.

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

Next, multiply that by the sample size of 732.

Z = (1581 - 3311)/860 = -2    

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b