(t-distribution) A manufacturing firm claims that the batteries used in laptop computers will last an average of 50 months. To m
1 answer:
Answer:
There is an 38.21% probability that we find this lifespan for our sample average, or something even shorter.
Step-by-step explanation:
Problems of normally distributed samples can be 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.
In this problem, we have that:
A manufacturing firm claims that the batteries used in laptop computers will last an average of 50 months. This means that .
We found that the sample had a average lifespan of 47.3 months, and a standard deviation of s = 9 months. What is the probability that we find this lifespan for our sample average, or something even shorter?
We have to find the pvalue of Z when .
We are working with a sample mean, so we use the standard deviation of the sample in the place of . That is
So
has a pvalue of 0.3821.
There is an 38.21% probability that we find this lifespan for our sample average, or something even shorter.
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Considering the given linear function, the inequality graphed is:
B. .
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:
m = (4 - 2)/(2 - 1) = 2.
Thus the equation of the line is:
y = 2x + 2.
The left-side of the line is the values above the line, hence the inequality is:
B. .
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
2640mm
Step-by-step explanation:
I'm assuming you need the area of the rectangle which the circles don't take up.
First, to find the area of the whole rectangle:
length x width
to find length:
the length is 1 circle, therefore it is the diameter of the circle, which is 32 x 2 = 64mm
to find width:
the width is 3 circles, which is the radius 6 times, so 32 x 6 = 192mm
So, area of rectangle = 64 x 192 = 12288mm
Now to find the area the circles take up:
area of 1 circle =
=
=
As we have 3 circles, we multiply this by 3:
Finally we subtract the area of the three circles from the area of the rectangle:
As we need to round it to 3 significant figures, the answer is 2640mm
Answer:
The 95% confidence interval for the mean breaking weight for this type cable is (767.47 lb, 777.13 lb).
Step-by-step explanation:
Our sample size is 41
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
Then, we need to subtract one by the confidence level and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 40 and 0.025 in the two-sided t-distribution table, we have
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
Now, we multiply T and s
Then
The lower end of the confidence interval is the mean subtracted by M. So:
The upper end of the confidence interval is the mean added to M. So:
The 95% confidence interval for the mean breaking weight for this type cable is (767.47 lb, 777.13 lb).