"if one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drin
k root beer."
2 answers:
the picture in the attached figure
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
P=size of the event space/size of the sample space
step 1
find the probability that the person is over 40 years
size of the sample size=255
size of the event space=85
P=85/255------> P=1/3
step 2
find the probability that they drink root beer
size of the sample size=255
size of the event space=75
P=75/255------> P=5/17
step 3
find the probability that the person is over 40 years of age or that they drink root beer
so
P=(1/3)+(5/17)-----> P=(17*1+3*5)/51------> P=32/51-----> 0.6275----> 62.75%
therefore
the answer is
32/51 or 62.75%
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Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have a 95% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:
Hence the bounds of the interval are:
As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
More can be learned about the z-distribution at brainly.com/question/25890103
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