"Each week, a subcommittee of four individuals is formed from among the members of a committee comprising seven individuals. Two
1 answer:
Answer:
140 weeks.
Step-by-step explanation:
We are being asked for the maximum number that can elapse without having 2 subcommitees with the same members and the same chair. Notice that the secretary is not mentioned in this statement, so we can ignore that position.
Now, the maximum number of weeks would be equal to the total possible combinations of subcommitees that can be formed from the 7 individuals commiteed, times the number of options that can sit at the chair possition.
The total possible combinations of subcommitees that can be formed from the 7 individuals can be expressed like the following expression. Notice that there is no a particular order to be considered, so we use the combination formula:
=
= 35
Now, each of the 4 individuals have the same probability of being chosen as the chair commitee. So, we have to multiply 4 times the number of possible subcommitees in order to arrive our answer:
x = 35 * 4 = 140
This would be the maximum number of subcommitees that can be formed with no subcommitees with the same members and the same chair occurring.
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Answer:
Step-by-step explanation:
Hello!
There are two variables of interest:
X₁: number of college freshmen that carry a credit card balance.
n₁= 1000
p'₁= 0.37
X₂: number of college seniors that carry a credit card balance.
n₂= 1000
p'₂= 0.48
a. You need to construct a 90% CI for the proportion of freshmen who carry a credit card balance.
The formula for the interval is:
p'₁±
0.37±1.648*
0.37±1.648*0.015
[0.35;0.39]
With a confidence level of 90%, you'd expect that the interval [0.35;0.39] contains the proportion of college freshmen students that carry a credit card balance.
b. In this item, you have to estimate the proportion of senior students that carry a credit card balance. Since we work with the standard normal approximation and the same confidence level, the Z value is the same: 1.648
The formula for this interval is
p'₂±
0.48±1.648*
0.48±1.648*0.016
[0.45;0.51]
With a confidence level of 90%, you'd expect that the interval [0.45;0.51] contains the proportion of college seniors that carry a credit card balance.
c. The difference between the width two 90% confidence intervals is given by the standard deviation of each sample.
Freshmen:
Seniors:
The interval corresponding to the senior students has a greater standard deviation than the interval corresponding to the freshmen students, that is why the amplitude of its interval is greater.