A sample of 10 adult elephants had an average weight of 12,556 pounds. The standard deviation

Mathematics

1 answer:

kirill [66]2 years ago

6 0

Answer:

The 99% confidence interval of the population mean for the weights of adult elephants is between 12,475 pounds and 12,637 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 3.25

The margin of error is:

M = T*s = 3.25*25 = 81

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 12,556 - 81 = 12,475 pounds

The upper end of the interval is the sample mean added to M. So it is 12,556 + 81 = 12,637 pounds.

The 99% confidence interval of the population mean for the weights of adult elephants is between 12,475 pounds and 12,637 pounds.

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Use the fraction strips to compare 2/4 and 5/8. use the drop-down menus to explain your comparison.

tia_tia [17]

Answer:

$\dfrac{4}{5}$

Step-by-step explanation:

We are given 2 fractional numbers:

$1.\ \dfrac{2}4\\2.\ \dfrac{5}8$

We have to use fraction strips to compare to the fractional numbers.

Let we are Comparing $\frac{2}{4}$ with the length of $x$ number of $\frac{1}4$ sections.

i.e.

$\dfrac{2}{4} = x \times \dfrac{1}{4}\\\Rightarrow x = \dfrac{2 \times 4}{4}\\\Rightarrow x = 2$

Let we are Comparing $\frac{5}{8}$ with the length of $y$ number of $\frac{1}8$ sections.

i.e.

$\dfrac{5}{8} = y \times \dfrac{1}{8}\\\Rightarrow y = \dfrac{5 \times 8}{8}\\\Rightarrow y = 5$

Now, let us have a look at 3rd part of question:

The sections of 2/4 is _____ the length of 5/8. Therefore, 2/4 < 5/8

Let the answer be $z$ .

So, the equation becomes:

$\dfrac{2}{4} = z \times \dfrac{5}{8}\\\Rightarrow z = \dfrac{2 \times 8}{4 \times 5}\\\Rightarrow z = \dfrac{2 \times 2}{5}\\\Rightarrow z = \dfrac{4}{5}$