9.
Facebook Friends:
Based on a study of U.S. Facebook users in 2014, the most connected age group were
Facebook users between 18 and 24 years, averaging 649 friends on the social media website. Assume the
distribution for the number of Facebook friends for this age group is approximately normal with mean of
649 friends and a standard deviation of 150 friends.
a.
Based on the model, determine the value that would correctly complete the sentence below.
[2]

Using the z table we find that a z score = 1.04 has an area to the left of 0.8500.
So we need to solve for the number of friends:
𝟏𝟏
.
𝟎𝟎𝟒𝟒
=
𝒙𝒙−𝟔𝟔𝟒𝟒𝟔𝟔
𝟏𝟏𝟓𝟓𝟎𝟎
, x = 649 + 1.04(150) = 802
Note: If they use z = 1.05 and get 803.5 it is ok.
Final Answer:
at least
______
802
______
friends
b. Based on the model, what is the probability that a randomly selected Facebook user between 18 to
24 years has at least 844 friends?
[2]

c. Consider a random sample of 8 Facebook users between 18 to 24 years. What is the probability that
exactly 3 of the 8 Facebook users will have at least 844 friends?
[3]

Stats 250 Fall 2016 Exam 1
Page 6 of 7
10.
Abandoning Landlines:
The Centers for Disease Control and Prevention reported that 41% of all U.S.
households use only cellphones (no landlines). Suppose this rate is indeed correct. A random sample of
60 U.S. households
will be
selected, and the sample proportion that use only cellphones
will be
computed.
a.
In order to understand if finding at least 50% of the sampled households use only cellphones would be
unusual, having a frame of reference would be helpful. Provide that frame of reference by giving a
complete sketch of the
approximate
distribution of the possible values for such a
sample proportion
.
Include a label for the x axis, a complete label for the distribution, and, using the empirical rule, provide
at least
three values along the x axis.
[3]
b.
Compute the
approximate
probability that at least 50% of the sampled households use only cellphones.
[3]
Using the approximate normal model for a sample proportion N(0.41,
�
(.
𝟒𝟒𝟏𝟏
)(
𝟏𝟏−
.
𝟒𝟒𝟏𝟏
)/
𝟔𝟔𝟎𝟎
)
or
N(0.41 , 0.0635) distribution.
So we need to standardize:
𝒛𝒛
=
𝟎𝟎
.
𝟓𝟓𝟎𝟎−𝟎𝟎
.
𝟒𝟒𝟏𝟏
𝟎𝟎
.
𝟎𝟎𝟔𝟔𝟑𝟑𝟓𝟓
= 1.42,
and the area to the right of z = 1.42 is found from z table as 1 – 0.9222 = 0.0778.
Final Answer: _____
0.0778
_____
11.
Reading Habits After High School:
A recent publication in
Time
magazine reported that 70% of high school
graduates read a book in the summer after graduation. The principal of Pioneer High School (PHS) asks the
AP statistics teacher to conduct a study to assess whether more than 70% of PHS graduates read a book in the
summer after graduation. The teacher will contact a random sample of 25 recent PHS graduates and record