Broward Community College
Math Dept.
Statistics STA2023
Example of Test # 2
1-) There are approximately 74.8 million dogs in the United States ("http://www.hsus.org/pets/"). The proportion of dogs in each household is given in the table.
X |
0 |
1 |
2 |
3 or more |
P(X) |
0.61 |
0.24 |
0.10 |
0.05 |
Considering
that the proportion of households with 4 or more dogs is zero, find the mean, standard deviation,
variance, and skewness of the distribution of dogs per household.
2-) Dentists
are increasingly concerned about the growing trend of local school districts to
grant soft drink companies exclusive rights to install soda pop machines in
schools in return for money-usually millions-that goes directly into school
coffers. According to a recent study by the National Soft Drink Association, 62%
of schools nationally already have such contracts. This comes at a time when
dentists are seeing an alarming increase in horribly decayed teeth and eroded
enamel in the mouths of teenagers and young adults. With ready access to soft
drinks, children tend to drink them all day. That, combined with no opportunity
to brush, leads to disaster, dentist say. Suppose that 20 schools around the
country are randomly selected and asked if they have a soft drink contract. Find
the probability that the number of “Yes” answers is:
a-) exactly 8
b-) at most 8
c-) at least 4
d-) between 4 and 12, inclusive
e-) Identify the random variable of interest, X. Then write the
probability distribution table for X
f-) Draw a probability histogram for X.
4-) For a given population of
high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a
mean score of 500 with a standard deviation of 100. Another widely used test is
the American College Testing (ACT) exam. The mathematics portion of the ACT has
a mean of 18 and a standard deviation of 6. Both SAT and ACT scores are normally
distributed. What is the probability that a randomly selected high school
senior’s score on the mathematics part of the SAT will be
(a)
more than 675?
(b)
less than 450
(c)
between 450 and 675?
What is the probability
that a randomly selected high school senior’s score on the mathematics part of
the ACT will be
(d)
more than 28?
(e)
More than 12?
(f)
Between 12 and 28?
5-) Coal is carried from a
mine in West Virginia to a power plant in New York in hopper cars on a long
train. The automatic hopper car loader is set to put 75 tons of coal in each
car. The actual weights of coal loaded into each car are normally distributed
with mean μ=75 tons and standard deviation σ= 0.8 ton.
(a)
What is the probability that one car chose at random will have less than
74.5 tons of coal?
(b)
What is the probability that 20 cars chosen at random will have a mean
load weight X = of less than 74.5 tons of coal?
(c)
Suppose that the weight of coal in one car was less than 74.5 tons. Would
that fact make you suspect that the loader had slipped out of adjustment?
(d) Suppose the weight of coal in 20 cars selected at random had an average X less
than 74.5 tons. Would that fact make you suspect that the loader had slipped out
of adjustment? Why?