Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 8 and 22 minutes, inclusive. Let X =
1 answer:
Answer:
And replacing we got:
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
Step-by-step explanation:
We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:
And for this case we want to find the following probability:
We can find this probability using the complement rule and the cumulative distribution function given by:
Using this formula we got:
And replacing we got:
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
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Answer: The system of equations has NO SOLUTION.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
Given the following system of equations:
Write the first equation and solve for "y" in order to express it in Slope-Intercept form:
You can identify that:
Apply the same procedure with the second equation. Then:
You can identify that:
The slopes of both lines are equal, therefore the lines are parallel and the system has NO SOLUTION.
Answer:
Step-by-step explanation:
Hello!
To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:
<u>Group 1</u>: Ate healthy breakfast
X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.
n₁= 26
<u>Group 2: </u>Did not eat healthy breakfast
X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.
n₂= 20
After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:
p'₁= 0.50
p'₂= 0.40
The parameters of study are the population proportions, if the claim is true then p₁ > p₂
And you can determine the hypotheses as
H₀: p₁ ≤ p₂
H₁: p₁ > p₂
α: 0.05
≈N(0;1)
pooled sample proportion:
p-value: 0.2514
The decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.
At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.
So having a healthy breakfast doesn't seem to improve the grades of students.
I hope this helps!