Question

The weights for newborn babies is approximately normally distributed with a mean of 6.9 pounds and a standard deviation of 1.1 pounds. Consider a group of 1200 newborn babies: 1. How many would you expect to weigh between 6 and 9 pounds? 2. How many would you expect to weigh less than 8 pounds? 3. How many would you expect to weigh more than 7 pounds? 4. How many would you expect to weigh between 6.9 and 10 pounds?

Answer 1

Here mean = = 6.9 pounds

standard deviation = = 1.1 pounds

(a) P(6 < x < 9) = P(x < 9 ; 6.9 ; 1.1) - P(x < 6; 6.9; 1.1)

= NORMDIST(9, 6.9, 1.1 true) - NORMDIST(6, 6.9,1.1, true)

= 0.971875 - 0.206627= 0.7652

expect to weigh between 6 and 9 pounds out of 1200 = 1200 * 0.7652 = 918.30

(b) P(x < 8) = NORMDIST(8, 6.9, 1.1 true) = 0.841345

expect to weigh between less than 8 pounds out of 1200 = 1200 * 0.841345 = 1009.6

(c) P(x > 7 pounds) = 1 - NORMDIST(7, 6.9, 1.1 true) = 1 - 0.5362 = 0.4638

expect to weigh more than 7 pounds out of 1200 = 1200 * 0.4638 = 556.54

(d) P(6.9 pounds < x < 10 pounds) = NORMDIST(10, 6.9, 1.1 true) - NORMDIST(6.9, 6.9,1.1, true)

= 0.9976 - 0.5 = 0.4976

expect to weigh between 6.9 pounds to 10 pounds out of 1200 = 0.4976 * 1200 =597.10