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3 years ago

Please help me with 4 and 5

Mathematics

1 answer:

Sedbober [7]3 years ago

3 0

Answer:

The answer to No. 4 is x = 12.

The answer to No. 5 is 160.

Step-by-step explanation:

(No. 4) The mean (average) is calculated by adding up all the numbers and then dividing by how many numbers there are.

In the first exercise, there are 6 number with a mean of 8.5. Since the mean is calculated by dividing the sum of the numbers by how many numbers there are, we know that the sum of the numbers have to be 8.5 × 6 = 51.

Subtracting all the known numbers from 51 leaves you with the only possible solution for x: 51 - 11 - 8 - 8 - 7 - 5 = 12.

(No. 5) Start by calculating the total mass of all the spiders. (16 × 175) + (24 × 150) = 6,400. Once again, to calculate the mean, divide the total sum of the numbers by how many numbers there are, in this case you divide the total mass of the spiders by how many spiders there are, leaving you with the average of 6,400 ÷ 40 = 160.

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And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$