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Problem 4 –Weights of newborn babies (6 marks) Paediatricians measure the weights of newborn babies to...

Problem 4 –Weights of newborn babies
Paediatricians measure the weights of newborn babies to closely monitor their growth in the first six months of their life. A study reveals that weights of newborn babies are normally distributed with a mean of 3.2kg and a standard deviation of 0.4kg.



a) Find the probability that a randomly selected newborn baby would have a weight more than 3.5kg. Display working. 1 mark



b) Eight newborn babies are randomly selected. What is the probability that their mean weight is between 3.2kg and 3.6kg? Display working. 1.5 marks



c) Six newborn babies are randomly selected. What is the probability that their mean weight is less than 3.0kg. Display working. 1.5 marks
d) Find the cut off weight for the 10% heaviest newborn babies. Display working.

2 marks
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a.

b.

c.

d.

Heaviest babies lies in the right tail of the distribution. It mean we want 90th percentile which separate 10% heaviest babies from remaining babies.

For standard normal distribution z = 1.28 is the 90th percentile.

We know that,

Hence cut off weight for the 10% heaviest newborn babies is 3.712

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