Statistics 104 - Laboratory 8
Normal Models
Often a population will have a variable whose distribution can be modeled using a normal
model with a population mean μ and a population standard deviation σ.
1. Market weight of gilts.
The market weight, in pounds, of 179 gilts, female hogs is displayed in the histogram
below.
Market Weight (lbs)
a) Describe the shape of the distribution. Why is a normal model a reasonable
model for the distribution of the population of gilt market weights?
b) Use a normal model for the population of gilt market weights with population
mean μ = 236.5 pounds and population standard deviation σ = 31.2 pounds to find
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The probability that a gilt market weight will be less than 300 pounds.
The probability that a gilt market weight will be greater than 275 pounds.
The probability that a gilt market weight will be between 200 and 300
pounds.
The value such that 4% of all gilt market weights will be less than that
value.
The value such that 25% of all gilt market weights will be greater than that
value.
The values such that the middle 90% of all gilt market weights will fall
between those values.
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2. Body Mass Index
The Body Mass Index is calculated from a person’s weight, in kilograms, and height, in
meters, and is positively correlated to the amount of body fat. BMI is often used to
classify individuals into a Weight Status category.
BMI
BMI below 18.5
18.5 ≤ BMI< 25.0
25.0 ≤ BMI< 30.0
BMI 30.0 and above
Weight Status
Underweight
Normal weight
Overweight
Obese
Below is information on BMI for young males age 20 to 29 and young females age 20
to 29 in the early 1960’s and the early 2000’s.
BMI
mean, μ
std. dev., σ
Early 1960’s
males
females
24.3
22.2
5.4
5.8
Early 2000’s
males
females
26.6
26.8
6.0
7.0
The distribution of BMI values can be described using a normal model.
a) What is the probability that a male chosen at random in 1960 was obese?
b) What is the probability that a male chosen at random in 2000 was obese?
c) What is the probability that a female chosen at random in 1960 was normal
weight?
d) What is the probability that a female chosen at random in 2000 was normal
weight?
e) What general trend do you see from 1960 to 2000 in terms of BMI and Weight
status?
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Statistics 104 - Laboratory 8
Group Answer Sheet
Names of Group Members:
____________________, ____________________
____________________, ____________________
1. Octane Rating
a) Describe shape and comment on why a normal model is reasonable.
b) The probability that a gilt market weight will be less than 300 pounds.
c) The probability that a gilt market weight will be greater than 275 pounds.
d) The probability that a gilt market weight will be between 200 and 300 pounds.
e) The value such that 4% of all gilt market weights will be less than that value.
f) The value such that 25% of all gilt market weights will be greater than that value.
g) The values such that the middle 90% of all gilt market weights will fall between
those values.
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2. Body Mass Index
a) What is the probability that a male chosen at random in 1960 was obese?
b) What is the probability that a male chosen at random in 2000 was obese?
c) What is the probability that a female chosen at random in 1960 was normal
weight?
d) What is the probability that a female chosen at random in 2000 was normal
weight?
e) What general trend do you see from 1960 to 2000 in terms of BMI and Weight
status?
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