Question

Question 6 (10 marks) Health Canada reported that the distribution of weights of newborns in Canada is approximately unimodal and approximately symmetrical with mean 3500 grams and standard deviations 500 grams. Ontario Medical Association defined very heavy birth weight babies (VHBWB) to be those weighing over 5000 grams, and low birth weight babies (LBWB) to be those weighing less than 2000 grams. a. Based on the given information, what percentage of newborns are either LBWB or VHBWB? b. Based on the given information, what is the birth weight that is exceeded by 16% of all newborns? If the distribution of weights of newborns in Canada is actually very skewed. What percentage of newborns are between 2500 grams and 4500 grams? c.

Answer 1

Ans:

Given that

mean=3500

standard deviation=500

a)

2000 and 5000 grams are 3 standard deviations below and above the mean respectively.

According to empirical rule,99.73% of the data falls within 3 standard deviations of the mean,so 0.27% falls outside it.

Hence,0.27% are either LBWB or VHBWB.

b)

According to empirical rule,68% of data falls within one standard deviation of the mean,so 32% falls beyond one standard deviations,so half of 32% i.e. 16% will exceeded by one standard deviation.

Hence, 16% of the newborns will be exceeded by 3500+500=4000 grams

c)

2500 and 4500 are 2 standard deviations below and above the mean respectively.

As,data is not normally distributed,so use Chebyshev's rule.

k=2

1-(1/k^2)=1-(1/2^2)=1-(1/4)=3/4=0.75 or 75% of newborns are between 2500 grams and 4500 grams.