## Data from the article “The Osteological Paradox: Problems inferring Prehistoric Health from Skeletal Samples” (Current Anthropology (1992):3

Data from the article “The Osteological Paradox: Problems inferring Prehistoric Health from Skeletal Samples” (Current Anthropology (1992):343-370) suggests that a reasonable model for the distribution of heights of 5-year old children (in centimeters) is N(100, 62) . Let the letter X represent the variable “height of 5-year old”, and use this information to answer the following. Use 4 decimal places unless otherwise indicated.

(a) P(X > 89.2) =

(b) P(X < 109.78) =

(c) P(97 < X < 106) =

(d) P(X < 85.6 or X > 111.4) =

(e) P(X > 103) =

(f) P(X < 98.2) =

(g) P(100 < X < 124)=

(h) The middle 80% of all heights of 5 year old children fall between and . (Use 2 decimal places.)

## Answers ( )

Answer:(a) P (X < 109.78) =

0.9484.(b) P (X < 109.78) =

0.9484.(c) P (97 < X < 106) =

0.5328.(d) P (X < 85.6 or X > 111.4) =

0.0369.(e) P (X > 103) =

0.3085.(f) P (X < 98.2) =

0.3821.(g) P (100 < X < 124) =

0.5000.(h) The middle 80% of all heights of 5 year old children fall between

92.31and107.70.Step-by-step explanation:It is provided that

Xfollows a Normal distribution with mean,μ= 100and standard deviation,σ= 6.(

a)Compute the value of P (X > 89.2) as follows:

Thus, the value of P (X > 89.2) is

0.9641.(

b)Compute the value of P (X < 109.78) as follows:

Thus, the value of P (X < 109.78) is

0.9484.(

c)Compute the value of P (97 < X < 106) as follows;

P (97 < X < 106) = P (X < 106) – P (X < 97)

Thus, the value of P (97 < X < 106) is

0.5328.(

d)Compute the value of P (X < 85.6 or X > 111.4) as follows;

P (X < 85.6 or X > 111.4) = P (X < 85.6) + P (X > 111.4)

Thus, the value of P (X < 85.6 or X > 111.4) is

0.0369.(

e)Compute the value of P (X > 103) as follows:

Thus, the value of P (X > 103) is

0.3085.(

f)Compute the value of P (X < 98.2) as follows:

Thus, the value of P (X < 98.2) is

0.3821.(

g)Compute the value of P (100 < X < 124) as follows;

P (100< X < 124) = P (X < 124) – P (X < 100)

Thus, the value of P (100 < X < 124) is

0.5000.(

h)Compute the value of

x₁ andx₂ as follows if P (x₁ < X <x₂) = 0.80 as follows:The value of

zis± 1.282.The value of

x₁ andx₂ are:Thus, the middle 80% of all heights of 5 year old children fall between

92.31and107.70.