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icang [17]
3 years ago
13

In a sample of 10 cabinets, the average height was found to be 37.3in. with a standard deviation of 3.

Mathematics
1 answer:
zysi [14]3 years ago
8 0

Answer:

\sigma^2 = 3^2 \frac{10-1}{10}= 8.10

Step-by-step explanation:

For this case we have a sample of n =10 and we have the following statistics:

\bar X = 37.3 , s= 3

And we want to estimate the population variance. We need to remember that the population variance is given by this formula:

\sigma^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}

And the sample variance is given by:

s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

And we can find a formula for the population variance in terms of the sample deviation like this:

\sigma^2 = s^2 \frac{n-1}{n}

And replacing we got:

\sigma^2 = 3^2 \frac{10-1}{10}= 8.10

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