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CDA認(rèn)證小程序

The daily office hours X (measured in hours) of employees in a certain department follow a normal distribution. The office hours for 6 employees on a particular day are as follows: 9, 10, 6, 7, 8.3, 7.7. Calculate the standard deviation of this sample (rounded to 2 decimal places).
A. 1.43
B. 1.42
C. 1.3
D. 1.3
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To calculate the sample standard deviation, subtract one degree of freedom. In this case, the denominator is 6-1=5.

要計(jì)算這6名員工的日常辦公時(shí)間的標(biāo)準(zhǔn)差,我們需要按照以下步驟進(jìn)行:

1. **計(jì)算樣本均值(平均值)**:
\[
\bar{X} = \frac{9 + 10 + 6 + 7 + 8.3 + 7.7}{6} = \frac{48}{6} = 8
\]

2. **計(jì)算每個(gè)樣本值與均值的差的平方**:
\[
(9 - 8)^2 = 1
\]
\[
(10 - 8)^2 = 4
\]
\[
(6 - 8)^2 = 4
\]
\[
(7 - 8)^2 = 1
\]
\[
(8.3 - 8)^2 = 0.09
\]
\[
(7.7 - 8)^2 = 0.09
\]

3. **計(jì)算這些差的平方的和**:
\[
1 + 4 + 4 + 1 + 0.09 + 0.09 = 10.18
\]

4. **計(jì)算樣本方差(使用樣本標(biāo)準(zhǔn)差公式)**:
\[
s^2 = \frac{\sum (X_i - \bar{X})^2}{n-1} = \frac{10.18}{6-1} = \frac{10.18}{5} = 2.036
\]

5. **計(jì)算樣本標(biāo)準(zhǔn)差**:
\[
s = \sqrt{s^2} = \sqrt{2.036} \approx 1.43
\]

因此,計(jì)算得到的樣本標(biāo)準(zhǔn)差是1.43,正確答案是 **A: 1.43**。