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Statistics Honors
Review of Section 7.1
Multiple Choice – Circle the letter that best answers each question.
A psychologist studied the number of puzzles subjects were able to solve in a five – minute period while
listening to soothing music. Let Xbe the number of puzzles completed successfully by a subject. The
psychologist found that X had the following probability distribution:
Value of X
Probability
1.)
3
0.3
4
0.1
0.3
0.4
0.6
0.9
Referring to the information above, P  X  3 has value:
(a)
(b)
(c)
(d)
3.)
2
0.4
Referring to the information above, the probability that a randomly chosen subject completes at
least three puzzles in the five – minute period while listening to the soothing music is:
(a)
(b)
(c)
(d)
2.)
1
0.2
0.3
0.4
0.6
0.9
Let the random variable X be a random number with the uniform density curve given below:
1
0
1
Referring to the information above, P  0.7  X  1.1 has value:
(a)
(b)
(c)
(d)
4.)
0.30
0.40
0.60
0.70
Let the random variable X represent the profit made on a randomly selected day by a certain store.
Assume X is normal with a mean of $360 and standard deviation $50. Referring to this
information, the value of P  X  $400  is:
(a)
(b)
(c)
(d)
0.2881
0.8450
0.7881
0.2119
Statistics Honors
5.)
Review of Section 7.1
In government data, a household consists of all occupants of a dwelling unit, while a family
consists of two or more persons who live together and are related by blood or marriage. So all
families form households, but some households are not families. Here are the distributions of
household size and family size in the United States:
Numbers of persons:
Household Probability:
1
2
3
4
5
6
7
0.25 0.32 0.17 0.15 0.07 0.03 0.01
Numbers of persons:
Family Probability:
1
0
2
3
4
5
6
7
0.42 0.23 0.21 0.09 0.03 0.02
(a)
Verify that each is a legitimate discrete probability function.
(b)
Make probability histograms for both distributions using the same scales. Label everything!
0.1
Household
(c)
Family
Choose an American household at random and let the random variable Y be the number
of persons living in the household.
Find P(Y>1)
(d)
What is P  2  Y  4  ?
(e)
What is P Y  2 
Statistics Honors
6.)
Review of Section 7.1
An opinion poll asks an SRS of 1500 adults, “Do you happen to jog?” Suppose that the
population proportion who jog is p  0.15 . In a large number of samples, the proportion p who
answer “Yes” will be N  0.15, 0.0092  .
Sketch this normal curve and use it to answer these questions:



P p  0.16
7.)
A psychologist studied the number of puzzles subjects were able to solve in a five – minute period
while listening to soothing music. Let X be the number of puzzles completed successfully by a
subject. The psychologist found that X had the following probability distribution:
Value of X
1
2
3
4
Probability
0.2
0.4
0.3
0.1
(b)
P 0.14  p  0.16

(a)
Briefly describe how you would use simulation to find P(X≤3). You must start by assigning
numbers to represent each value of X and then explaining the method you would use after that.
You are not carrying out the simulation, but you must describe in detail.
Assign numbers:
Method:
8.)
Suppose X is a continuous random variable taking values between 0 and 2 and having the
probability density function below:
Find: P(0.5  X  2)
1
0
2