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julia-pushkina [17]

3 years ago

8

(Brainliest Award) Suppose a sample of 225 was taken from a population with a standard deviation of 75 feet. In this case, the s

ample mean will be within 10 feet of the population mean 99.7% of the time.
A: True
B: False

2 answers:

strojnjashka [21]3 years ago

7 0

False!!
Hope This Helped!

Sedbober [7]3 years ago

6 0

Answer with explanation:

Sample Population = 225

Standard Deviation =75 feet

We have to check , whether , the sample mean, will be within 10 feet of the population mean, 99.7%=0.997 of the time.

$Z_{0.997}=0.83891$

$Z_{0.997}=\frac{\bar X-\mu}{\sigma}\\\\0.83891=\frac{225 -\mu}{75}\\\\75 \times 0.83891=225 - \mu\\\\ \mu=225 - 62.92\\\\ \mu=162.08$

Sample Mean =162 feet (Approx)

Assuming sample sample size is 2 times of sample Population.That is from ,450 , Sample of 250 is chosen.

Since, within three standard deviation ,from mean on both sides, the whole Population lies.

So, population Mean=225

Difference between Population mean and Sample Mean

→225 - 162= 63

Therefore, the Sample mean and population mean does not differ by a value of 10.

→Sample mean does not lie, within 10 feet of the population mean.

⇒The given statement is" false",which is ,the sample mean will be within 10 feet of the population mean 99.7% of the time.

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