Question

Assume newborn baby weights are Normally distributed with a mean of 7.6lbs and a variance of 0.6 lbs. Find the probability a newborn baby weighs over 10lbs or below 8 lbs.

Answer 1

Answer Date: 14/04/2020 The probability of a newborn baby weighs over 10 lbs or below 8 lbs is, First compute the over 10 lbs and below 8 lbs then take sum of both probabilities. The probability of a newborn baby weighs over 10 lbs is, First, compute the z score then find probability based on standard normal table. For x = 10 converts to 10-7.60 0.60 = 3.10 From the standard normal distribution table, the associated probability is 0.9990. Since find the area to the right, so subtract from 1 to get,

P(Z > 3.10)=1-(z<3.10) =1-0.9990 = 0.0010 The probability of a newborn baby weighs over 10 lbs is 0.0010. The probability of a newborn baby weighs below 8 lbs is, By using Excel software, find probability with the help of the following steps: 1) Import the data. Select NORMDIST from Functions. Enter X, Mean, Standard_dev and enter TRUE in Cumulative. 4) Click Ok. NORMDIST x Mean 7.60 Standard_dev 0.7746 Cumulative TRUE 6 * E - 8 = 7.6 = 0.7746 = TRUE = 0.697210917

From the Excel output, the probability of a newborn baby weighs below 8 lbs is 0.6972. The probability of a newborn baby weighs over 10 lbs or below 8 lbs is, p(x >10) or p(x<8) = p(x >10)+ p(x<8) = 0.0010 +0.6972 = 0.6982 The probability of a newborn baby weighs over 10 lbs or below 8 lbs is 0.6982.