Question

 

1) babies at risk weights of new born babies in the United States are normally distributed with a mean of 3420 g and a standard deviation of 495(based on data from "birth weight and prenatal mortality" by Wilcox et al., journal of the American medical association, via. 273 No.9). A newborn weighing less than 2200 g is considered to be at risk, because the mortality rate for this group is at least 1%. what percentage of newborn babies are in the "at-risk" category? if the Chicago general hospital has 900 births in a year. how many of the babies are in the "at-risk" category?

2) Measurements of human skulls from different epochs are analyzed to determine whether they change over time. The maximum breadth is measured for skulls from Egyptian males who lived around 3300 B.C. Results show that those breadths are normally distributed with a mean of 132.6 mm and a standard deviation of 5.4 mm. An archeologist discovers a male Egyptian skull and a field measurement reveals a maximum breadth of 124 mm. Find the probability of getting a value of 124 mm or less if a skull is randomly selected from the period around 3300 B.C. Is the newly found skull likely to come from that era?

Answer 1

1) Let X be the weight of a baby

then

= P(z < -2.46)

= 0.0070 (from z table)

Percentage of babies are at risk category = 0.70%

Out of 900 babies , number of babies at risk category are =6.3

2) Let X be the breadth of a skull

then

= P(z < -1.59)

= 0.0559     (from z table)

Probability of getting 124 mm or less from 3300BC = 0.0559

The probability though very less but greater than 0.05

P(X<125) >0.05 , which implies that the probability of getting skull breadth 124 mm or less is very small but not impossible.

Thus it cannot be concluded that the newly found skull is not from that era

Or otherwise we can say that , the newly found skull is likely to come from that era.