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Citrus2011 [14]
3 years ago
13

Assuming that it is known from previous studies that σ = 4.5 grams, how many mice should be included in our sample if we wish to

be 95% confident that the mean weight of the sam- ple will be within 3 grams of the population mean for all mice subjected to this protein diet?
Mathematics
1 answer:
Yuki888 [10]3 years ago
6 0

Answer:

The required amount of mice is 11.82 gram.

Step-by-step explanation:

Given : Assuming that it is known from previous studies that σ = 4.5 grams. If we wish to be 95% confident that the mean weight of the sample will be within 3 grams of the population mean for all mice subjected to this protein diet.

To find : How many mice should be included in our sample?

Solution :

The formula used in the situation is

z=\frac{x-\mu}{\sigma}

Where, z value at 95% confidence interval is z=1.96

\mu=3 gram is the mean of the population

\sigma=4.5 gram is the standard deviation of the sample

Substituting the value, to find x sample mean

1.96=\frac{x-3}{4.5}

1.96\times 4.5=x-3

8.82=x-3

x=8.82+3

x=11.82

Therefore, The required amount of mice is 11.82 gram.

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\frac{11}{87}

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125 divided by 32 equals what
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32 × 2 = 68
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So far we can conclude that the answer to your question lies somewhere between the numbers 3 and 4. To narrow down the answer some more, multiply 32 by 3.5 (a midway point between 3 and 4).

32 × 3.5 = 112
The number 112 tells us that the decimal we are looking for is higher than 3.5. (Because we need to get to 125, not 112.) Let's try some decimals between 3.5 and 4.

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With our midway point we can see that our number lies between 3.906 and 3.9065. Let's try a quarter point to see where our number lies from there.

32 × 3.90625 = 125
And BINGO! We have found the answer to the question. To be rephrased, our answer can be put like this:

\frac{125}{32} = 3.90625
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