设某天平的测量值服从正态分布N($\mu,\frac{1}{8}
$),用该天平测量物体甲与物体乙的质量，分别独立地测量4次，测得的
平均质量分别为5.5克与5.2克，则两物体质量差置信水平0.95的置信区间为（）
A: $(0.3 - \frac{1}{8}{u_{0.975}},0.3 + \frac{1}{8}{u_{0.975}})$
B: $(0.3 - \frac{1}{8}{u_{0.625}},0.3 + \frac{1}{8}{u_{0.625}})$
C: $(0.3 - \frac{1}{4}{u_{0.975}},0.3 + \frac{1}{4}{u_{0.975}})$
D: $(0.3 - \frac{1}{}{u_{0.625}},0.3 + \frac{1}{4}{u_{0.625}})$
$),用该天平测量物体甲与物体乙的质量，分别独立地测量4次，测得的
平均质量分别为5.5克与5.2克，则两物体质量差置信水平0.95的置信区间为（）
A: $(0.3 - \frac{1}{8}{u_{0.975}},0.3 + \frac{1}{8}{u_{0.975}})$
B: $(0.3 - \frac{1}{8}{u_{0.625}},0.3 + \frac{1}{8}{u_{0.625}})$
C: $(0.3 - \frac{1}{4}{u_{0.975}},0.3 + \frac{1}{4}{u_{0.975}})$
D: $(0.3 - \frac{1}{}{u_{0.625}},0.3 + \frac{1}{4}{u_{0.625}})$
举一反三
- 设总体X~N($\mu,{\sigma}^2$),$\mu,{\sigma}^2$未知，$x_{1},x_{2},...,x_{n} $ 是来自该总体的样本，记$\overline x=\frac{1}{n}\sum\limits_{i = 1}^{n}{x_{i}}$,则对假设检验$ H_{0}:u=u_{0},H_{1}:u!=u_{0}$的拒绝域为()
- 将函数\(f(x)=\sin^4 x\)展开成Fourier级数为 ____ . A: \(f(x) = \frac{3}{8}-\frac{1}{2}\cos 2x +\frac{1}{8}cos 4x\) B: \(f(x) = \frac{1}{4}-\frac{1}{2}\cos x +\frac{3}{8}cos 4x\) C: \(f(x) = \frac{1}{4}-\frac{1}{2}\sin 2x -\frac{3}{8}cos 4x\) D: \(f(x) = \frac{3}{8}-\frac{1}{2}\sin x -\frac{1}{8}cos 4x\)
- 当$|z|<0.5$时左边序列$x[n]$为 A: $[(\frac{1}{2})^n-2^n]u[-n-1]$ B: $[(\frac{1}{2})^n+2^n]u[-n-1]$ C: $[2^n-(\frac{1}{2})^n]u[-n-1]$ D: $[2^n+(-\frac{1}{2})^n]u[-n-1]$
- (1). 随机往单位圆内投针，针落在中心 \( \frac{1}{2} \)<br/>单位圆的概率为（ ）。 A: \( 1 \) B: \( \frac{1}{2} \) C: \( \frac{1}{4} \) D: \( \frac{1}{8} \)
- Solve $\int_{-\frac{1}{2}}^1{1-x^2}dx=$? A: $\frac{\pi}{3}+\frac{\sqrt{3}}{8}$. B: $\frac{\pi}{2}$. C: $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$. D: $\frac{\pi}{4}$.