Please help me with 1-4

Mathematics

1 answer:

dsp734 years ago

8 0

For problem 1, it will be 25/100, which is equal to 25%
2) The relationship is that both, the bar model and the proportion, show that x is 1/4 of the actual amount. The bar graph is more a visual. However, in both cases, the x can be solved for to be 25%
3) The percent error for 23°C will be less since it is closer to 25°C, the actual amount. The percent error is greater for 5°C since it is farther for 25°C.

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83 random samples were selected from a normally distributed population and were found to have a mean of 32.1 and a standard devi

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Answer:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.525 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.127 \leq \sigma \leq 2.757$

Step-by-step explanation:

Information given

$\bar X=32.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.4 represent the sample standard deviation

n=83 represent the sample size

Confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom given by:

$df=n-1=8-1=7$

The confidence level 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 values.