課程名稱︰統計學一
課程性質︰系必修
課程教師︰陳郁慧
開課學院：
開課系所︰
考試日期（年月日）︰2010.10.26
考試時限（分鐘）：70分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. The following data represent the number of appointments made for 15-minutes
interval by telephone solicitation for a lawn-care company. Assume these
are population data.
Number of Appointments Frequency of Occurrence
─────────────────────────────
0-under 1 31
1-under 2 57
2-under 3 26
3-under 4 14
4-under 5 6
5-under 6 3
─────────────────────────────
a. Calculate the mean of the data. (5%)
b. Calculate the mode. (5%)
c. Calculate the median. (5%)
d. Calculate the variance. (5%)
e. Calculate the standard deviation. (5%)
2. The U.S. Energy Department states that 60% of all U.S. houesholds have
ceiling fans. In addition, 29% of all U.S. households have an outdoor
grill. Suppose 13% of all U.S. households have both a ceiling fan and an
outdoor grill. A U.S. household is ramdomly selected.
a. What is the probability that the household has a ceiling fan or an
outdoor grill? (5%)
b. What is the probability that the household has neither a ceiling fan nor
an outdoor grill? (5%)
c. What is the probability that the household does not have a ceiling fan
and does have an outdoor grill? (5%)
d. What is the probability that the household does have a ceiling fan and
does not have an outdoor grill? (5%)
3. The Steelcase Workplace Index studied the type of workre-lated activities
that Americans did while on vacation in the summer. Among other things, 40%
read work-related material. Thirty-four percent checked in with the boss.
Respondents to study were allowed to selet more than one activity. Suppose
that of those who read work-related material, 78% checked in with the boss.
one of these survey respondents is selected randomly:
a. What is the probability that while on vacation this respondent checked in
with the boss and read work-related material? (5%)
b. What is the probability that while on vacation this respondent neither
read work-related material nor check in with the boss? (5%)
c. What is the probability that while on vacation this respondent read
work-related material given that respondent checked in with the boss?(5%)
d. What is the probability that while on vacation this respondent did not
check in with the boss given that the respondent read work-related
material? (5%)
e. What is the probability that while on vacation this respondent did not
check in with the boss given that the respondent did not read
work-related material? (5%)
f. Construct a probability matrix for this problem. (5%)
4. Suppose 70% of all companies are classified as small companies and large
companies. Suppose futher, 82% of the large companies provide training to
employees, but only 18% of small companies provide training. A company is
randomly selected without knowing if it is a large or small company.
However, it is determined that the company provides training to employees.
What are the prior probabilities that the companies is a large or small
company? (5%) What are the revised probabilities that the company is large
or small? (12%) Based on your analysis, what is the overall percentage of
companies that offer training? (8%)
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