Question

The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and a standard deviation of 1.4 pounds.

Consider a group of 1100 newborn babies:

1. How many would you expect to weigh between 4 and 8 pounds?

2. How many would you expect to weigh less than 7 pounds? 

3. How many would you expect to weigh more than 6 pounds? 

4. How many would you expect to weigh between 6.4 and 10 pounds? 

Answer 1

The weights for newborn babies are approximately normally distributed with a mean of 6.4 pounds and a standard deviation of 1.4 pounds. The number of newborn babies is n=1100 Let X be the weight4, of new born babies. 1) Calculate how many would you expect to weigh between 4 and 8 pounds. P(4< X <8)=P(X <8)- P(X <4) =pl X-4-8-6.4 -P(X-44-6.4) lo 1.4 To 1.4) Use Excel function = P(Z <1.1429) - P(Z <-1.7143) NORMSDIST(-) for getting p-value = NORMSDIST (1.1429) - NORMSDIST(-1.7143) = 0.8735 -0.0432 = 0.8302 Number of babies would expect to weigh between 4 and 8 pounds is 1100x 0.8302 2914 -<- Calculate How many would you expect to weigh less than 7 pounds. P(X <7)=P(X-4-7-6.4) o 1.4 = P(Z <0.4286) = NORMSDIST (0.4286) = 0.6659 Number of babies would expect to weigh less than 7 is 11000.6659 2733 Calculate How many would you expect to weigh more than 6 pounds. - < P(X>6)=1-P(X 56) =1-PX-46-6.4) o14 =1-P(Z <-0.2857) = 1- NORMSDIST (-0.2857) = 1-0.3875 = 0.6125 Number of babies would expect to weigh more than 6 is 1100*0.6125674 Calculate How many would you expect to weigh between 6.4 and 10 pounds. - - H - <- P(6.4 < X <10)=P(x <10)- P(X 56.4) =pl X-ų10-6.4)-pX-< 6.4–6.4) lo - 1.4 TO 1.4 [Use Excel function] = P(Z < 2.5714)- P(Z <0.0000) NORMSDIST(z) (for getting p-value = NORMSDIST (2.5714)- NORMSDIST (0) = 0.9949-0.5000 = 0.4949 Number of babies would expect to weigh between 4 and 8 pounds is 1100*0.4949 - 545