What is the area of this figure
2 answers:
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Answer:
50.34% probability that the sample mean would differ from the true mean by less than 1.1 months
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months
This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So
X = 120.1
By the Central Limit Theorem
has a pvalue of 0.7517
X = 117.9
has a pvalue of 0.2483
0.7517 - 0.2483 = 0.5034
50.34% probability that the sample mean would differ from the true mean by less than 1.1 months
Answer: y-intercept: (0, 12)
Step-by-step explanation:
= 9 − 3 (n − 1)
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
y = mx + b
Find the values of m and b using the form y = mx + b.
m = −3
b = 12
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: −3
intercept: (0, 12)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Find the x-intercept.
To find the x-intercept(s), substitute in 0 for y and solve for x.
0 = −3x + 12
Solve the equation.
Rewrite the equation as −3x + 12 = 0.
−3x + 12 = 0
Subtract 12 from both sides of the equation.
−3x = −12
Divide each term by −3 and simplify.
x = 4
x-intercept(s) in point form.
x-intercept(s): (4, 0)
Find the y-intercept.
To find the y-intercept(s), substitute in 0 for x and solve for y.
y = −3 ⋅ 0 + 12
Solve the equation.
Remove parentheses.
y = −3 ⋅ 0 + 12
Simplify −3 ⋅ 0 + 12.
y = 12
intercept(s) in point form.
intercept(s): (0, 12)
Create a table of the x and y values.
<u> x | y </u>
0 | 12
4 | 0
Graph the line using the slope and the y-intercept, or the points.
Slope: −3
intercept: (0, 12)
