Mathematics, 02.04.2020 02:08 Pookiev

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

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Answer from: tonypewitt

95% confidence interval for the true mean cholesterol content of all such eggs is [173.82 , 196.18].

Step-by-step explanation:

We are given that a laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ t_n_-_1

where, $\bar X$ = sample mean amount of cholesterol = 185 milligrams

s = sample standard deviation = 17.6 milligrams

n = sample of chicken eggs = 12

$\mu$ = true mean

Here for constructing 95% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.201 < t_1_1 < 2.201) = 0.95 {As the critical value of t at 11 degree of

freedom are -2.201 & 2.201 with P = 2.5%}

P(-2.201 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.201) = 0.95

P( $-2.201 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.201 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.201 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.201 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.201 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.201 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $185-2.201 \times {\frac{17.6}{\sqrt{12} } }$ , $185+2.201 \times {\frac{17.6}{\sqrt{12} } }$ ]

= [173.82 , 196.18]

Therefore, 95% confidence interval for the true mean cholesterol content of all such eggs is [173.82 , 196.18].

Answer from: Quest

In the first triangle 80+20+p=180 (since sum of all angles of a triangle is 180)so p= 80also in second triangle 55+45+q=180 (since sum of all angles of a triangle is 180)so q=80so we can conclude that p=80 degrees q=80 degrees so p=q=80 degreeshence option b is correct
What do you know to be true about the values of p and q?

What do you know to be true about the values of p and q?

Answer from: Quest

A. p = 2(l + w)p/2 - l = ww = p/2 - l b. while isolating the variable w in the equation, i first divided both sides by 2 and then i subtracted l from both sides. i hope this .

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A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 millig...