One member of the debate team is going to be chosen president. each member is equally likely to be chosen. the probability that
a girl is chosen is 2/3 the probability that a boy is chosen. if the debate team has 20 people, how many girls are there?
1 answer:
Let
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>
we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2
t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4
resolve the equations system
x=B/20
(2/3)*x=[20-B]/20
using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8
number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%
the answer is
number of girls in the debate team is 8
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>
we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2
t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4
resolve the equations system
x=B/20
(2/3)*x=[20-B]/20
using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8
number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%
the answer is
number of girls in the debate team is 8
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Answer:
So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:
