Generating...                               quiz02_n19

  1. The germination time in days of a newly planted seed has the mean value of $2$ and variance $4$. If the germination times $X_1,\ldots,X_n$ are independent, find the mean and the variance for the average germination time $\bar{X}$ of $n = 100$ seeds.

    The mean is ${{1}\over{2}}$ and the variance is ${{4}\over{25}}$ The mean is ${{1}\over{2}}$ and the variance is ${{1}\over{25}}$ The mean is $2$ and the variance is ${{4}\over{25}}$ The mean is ${{1}\over{2}}$ and the variance is $4$ The mean is $2$ and the variance is ${{1}\over{25}}$ The mean is $2$ and the variance is $4$

  2. Let $X$ be a normal random variable with $\mu = 10$ and $\sigma = 10$. Find $P( 20 < X < 30)$.

    $0.9772 - 0.8413 = 0.1359$ $0.9974 - 0.9641 = 0.0334$ $1.0 - 0.9772 = 0.0227$ $1.0 - 0.9998 = 2.0 \times 10^{-4}$

  3. Let $Z$ be a standard normal random variable. Find the value of $x$ such that $P(Z > x) = 0.01$.

    $1.64$ $3.28$ $2.33$ $4.66$

  4. The germination time in days of a newly planted seed has the mean value of ${{9}\over{2}}$ and variance ${{9}\over{4}}$. If the germination times $X_1,\ldots,X_n$ are independent, estimate the probability that the average germination time $\bar{X}$ of $n = 36$ seeds is between 4.7 and 5.2 days.

    $\Phi( 1.83) - \Phi( 0.17) \approx 0.4004$ $\Phi( 2.8) - \Phi( 0.8) \approx 0.2093$ $\Phi( 2.2) - \Phi( 0.2) \approx 0.4068$ $\Phi( 2.33) - \Phi( 0.67) \approx 0.2427$

  5. An actual voltage of new battery has the mean value of $6$ and the variance ${{4}\over{3}}$. Consider the the average voltages from 10 new batteries. Find the mean and the variance.

    The mean is ${{3}\over{5}}$ and the variance is ${{1}\over{10}}$ The mean is $6$ and the variance is ${{2}\over{15}}$ The mean is ${{3}\over{5}}$ and the variance is ${{2}\over{15}}$ The mean is $6$ and the variance is $10$ The mean is ${{3}\over{5}}$ and the variance is $10$ The mean is $6$ and the variance is ${{1}\over{10}}$


Department of Mathematics
Last modified: 2025-06-01