Question

Babies' birth weight follows a normal law, with an average of 6 pounds and a standard deviation 1 pound.

a) Calculate the probability of a newborn baby weighing more than 5 pounds.

b) Out of 50 babies, what is the probability that at least 47 of them weigh more than 5 pounds?

c) In order to eradicate obesity, a dictator decides to eliminate 10% of babies at birth, 10% heavier. What is the weight of the largest surviving baby?

Answer 1

It is given that the birth weight folows a Normal distribution with .

a). The probability of a newborn baby weighing more than 5 pounds.

We know that the standard Normal variate corersponding to 5 is

Theerfore

  

  

The probability of a newborn baby weighing more than 5 pounds=0.8413.

b) Out of 50 babies, what is the probability that at least 47 of them weigh more than 5 pounds?

We know that The probability of a newborn baby weighing more than 5 pounds=0.8413 and let us call it as a success(p) for the purpose of the Binomial pouplation. therefore the The probability of a newborn baby weighing less than 5 pounds(1-p)=1-0.8413=0.1587.

We have n=50 and we need to find out the

I had made the EXCEL sheet to calculate the quantities needed for this. You may delete it while submitting or can leave it if you need.

x	n-x	p	q	p*q	ncx	pb
47	3	0.000297	0.003997	1.18692E-06	19600	0.023264
48	2	0.00025	0.025186	6.29211E-06	1225	0.007708
49	1	0.00021	0.1587	3.33557E-05	50	0.001668
50	0	0.000177	1	0.000176825	1	0.000177
						0.032816

Therefore,Out of 50 babies, the probability that at least 47 of them weigh more than 5 pounds =0.0328.

(c) Eliminate 10% of babies at birth, 10% heavier. What is the weight of the largest surviving baby?

Here we need to find out the such that

From the tables r EXCEL function NORM.S.INV(0.9), we can find out this value as 1.2816.

Therefore is the weight of the largest surviving baby.