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Homework 1 (MATH 4255-01)
Due date: Tuesday, Feb. 2, 2010
Name (Print):
1. Temperature measurements (in C) result in the following numbers Ni of temperature
values which where found in a certain temperature interval Ti:
Ti 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26
Ni
500 1400 2200 3600 5000 3300 2600 1300 300
a) Calculate the mean of the temperature distribution.
b) Calculate the standard deviation of the temperature distribution.
c) Assume that the temperature distribution can be described by normal distribution.
Make a plot of the normal probability density function (PDF) that corresponds to
the given data set.
d) Calculate approximately the probability P(16  T  22) to find T between 16C and
22C.
Solutions:
a) <T> = 16.94;
b)  = 3.5;
d) P(16  T  22) = 53.2%
2. According to the National Health Survey, the heights of adult males in the United
States are normally distributed with mean 69.0 inches and standard deviation 2.8
inches.
a) What is the probability that an adult male chosen at random is between 65 inches
and 73 inches tall?
b) What percentage of the adult male population is more than 6 feet tall?
Solutions:
a) P(65  X  73) = 84.7%;
b) P(72  X  ) = 14.2%;
3. Boxes are labeled as containing 500 g of cereal. The machine filling the boxes
produces weights that are normally distributed with standard deviation 12 g.
a) If the target weight is 500 g, what is the probability that the machine produces a box
with less than 480 g of cereal?
b) Suppose a law states that no more than 5% of a manufacturer’s cereal boxes can
contain less than the stated weight of 500 g. At what target weight should the
manufacturer set its filling machine?
Solutions:
a) P(0  X  480) = 4.78%;
b) <X> = 520 g;