At your school, 20% of the class are marketing majors. You are randomly assigned to two partners in your statistics class. a)
1 answer:
Answer:
a) 20%
b) 80%
c) There is 4% probability that both will be marketing majors.
d) There is a 36% probability that at least one will be a marketing major.
Step-by-step explanation:
At your school, 20% of the class are marketing majors.
This means that for each student, there is a 20% that he is a marketing major and an 80% chance that he is not a marketing major.
a) What is the probability that the first partner will be a marketing major?
The probabilities for each student are independent, so it is 20%.
b) What is the probability that the first partner won't be a marketing major?
80%
c) What is the probability that both will be marketing majors?
For each one, it is 20%. So:
There is 4% probability that both will be marketing majors.
d) What is the probability that at least one will be a marketing major?
That is one of them or both. For both, we found in c) that it is 4%.
For one of them, there are two cases. Either the first partner is and the second is not, or the other way. So, the probability that at least one will be a marketing major is
There is a 36% probability that at least one will be a marketing major.
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Let's start first by writing down the given:
σ = 100
sample mean = 450
sample size = 25
These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.
A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.
Next, we look for the standard error of the mean. This will have a formula
The standard error would just therefore be equal to
Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
ANSWER: 417.1<μ<482.9
σ = 100
sample mean = 450
sample size = 25
These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.
A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.
Next, we look for the standard error of the mean. This will have a formula
The standard error would just therefore be equal to
Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
ANSWER: 417.1<μ<482.9