Mathematics, 14.04.2020 21:34 montesa0910

25 men from Pinellas County were randomly drawn from a population of 100,000 men and weighed. The average weight of a man from the sample was found to be 150 pounds with a standard deviation of 54 pounds, Assuming the survey follows a normal distribution, find the 95% confidence interval for the true mean weight of men.

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Answer from: savannahvargas512

95% confidence interval for the true mean weight of men is [127.71 pounds , 172.30 pounds].

Step-by-step explanation:

We are given that the average weight of a man from the sample was found to be 150 pounds with a standard deviation of 54 pounds

25 men from Pinellas County were randomly drawn from a population of 100,000 men.

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 average weight of a man = 150 pounds

s = sample standard deviation = 54 pounds

n = sample of men = 25

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

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

P(-2.064 < t_2_4 < 2.064) = 0.95 {As the critical value of t at 24 degree of

freedom are -2.064 & 2.064 with P = 2.5%}

P(-2.064 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.064) = 0.95

P( $-2.064 \times }{\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.064 \times }{\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.064 \times }{\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.064 \times }{\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.064 \times }{\frac{s}{\sqrt{n} } }$ , $\bar X+2.064 \times }{\frac{s}{\sqrt{n} } }$ ]

= [ $150-2.064 \times }{\frac{54}{\sqrt{25} } }$ , $150+2.064 \times }{\frac{54}{\sqrt{25} } }$ ]

= [127.71 pounds , 172.30 pounds]

Therefore, 95% confidence interval for the true mean weight of men is [127.71 pounds , 172.30 pounds].

Answer from: Quest

hi, i am not sure about this one but i think its d,

hope this !

Which figure. does not appear to be congruent to the figure below

Answer from: Quest

to find the unit price, we must figure out the cost of one item (in this case one dish towel). to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

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25 men from Pinellas County were randomly drawn from a population of 100,000 men and weighed. The av...