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14 days ago

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It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impa

tient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
A. 5/8 + 5r = 8
B. 5/8 + 5r = 1
C. 5(5/8) = r
D. 5/8 = 5r

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A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one at a time and with replacem

lawyer [12517]

Answer:

$\mu _{\hat{p}}= 0.275\\\\ \sigma_{\hat{p}}=0.1997$

Step-by-step explanation:

It is known that the mean and standard deviation of the sampling distribution of the sample proportion( $\hat{p}$ ) are represented as follows:-

$\mu _{\hat{p}}=p\\\\ \sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}$

, where p= Population proportion and n = sample size.

Let p denote the proportion of blue chips.

According to the information provided, we have

p= 0.275

n= 5

Thus, the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 will be:

$\mu _{\hat{p}}= 0.275\\\\ \sigma_{\hat{p}}=\sqrt{\dfrac{ 0.275(1- 0.275)}{5}}\\\\=0.19968725547\approx0.1997$

Therefore, you will have the mean and standard deviation for the sample proportion of blue chips for samples of size 5:

$\mu _{\hat{p}}= 0.275\\\\ \sigma_{\hat{p}}=0.1997$

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2 months ago