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olya-2409 [2.1K]

3 years ago

12

A human hair was measured to be 8.0×10−4 inch thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the

thickness of the cat hair than the human hair? Write the answer in standard form.
The cat hair is
times thicker than the human hair.

1 answer:

Vera_Pavlovna [14]3 years ago

7 0

Answer:

A human hair was measured to be 8.0×10−4 inch thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the thickness of the cat hair than the human hair? Write the answer in standard form.

The cat hair is

times thicker than the human hair.

Step-by-step explanation:

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$42-1.833\frac{6.325}{\sqrt{10}}=38.334$

$42+1.833\frac{6.325}{\sqrt{10}}=45.666$

The 90% confidence interval is given by $38.334 \leq \mu \leq 45.666$

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Confidence interval

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=42$

The sample deviation calculated $s=6.325$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The Confidence level is 0.90 or 90%, the significance is $\alpha=0.1$ and $\alpha/2 =0.05$ , and the critical value would be $t_{\alpha/2}=1.833$

Replacing we got:

$42-1.833\frac{6.325}{\sqrt{10}}=38.334$

$42+1.833\frac{6.325}{\sqrt{10}}=45.666$

The 90% confidence interval is given by $38.334 \leq \mu \leq 45.666$

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