Generating...                               quiz02_n19

  1. An actual voltage of new battery has the mean value of $9$ and the variance ${{4}\over{3}}$. Consider the the average voltages from 20 new batteries. Find the mean and the variance.

    The mean is $9$ and the variance is $20$ The mean is ${{9}\over{20}}$ and the variance is $20$ The mean is ${{9}\over{20}}$ and the variance is ${{1}\over{15}}$ The mean is ${{9}\over{20}}$ and the variance is ${{1}\over{20}}$ The mean is $9$ and the variance is ${{1}\over{20}}$ The mean is $9$ and the variance is ${{1}\over{15}}$

  2. Let $Z$ be a standard normal random variable. Find the value of $x$ such that $P(Z > x) = 0.05$.

    $1.64$ $0.82$ $0.64$ $1.28$

  3. 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, estimate the probability that the average germination time $\bar{X}$ of $n = 36$ seeds is between 1.4 and 2.6 days.

    $\Phi( 1.2) - \Phi( -2.4) \approx 0.8767$ $\Phi( 1.0) - \Phi( -2.0) \approx 0.8186$ $\Phi( 1.8) - \Phi( -1.8) \approx 0.9281$ $\Phi( 1.5) - \Phi( -1.5) \approx 0.8664$

  4. The germination time in days of a newly planted seed has the mean value of $8$ and variance $16$. 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 $n = 25$ seeds.

    The mean is $8$ and the variance is ${{16}\over{25}}$ The mean is $8$ and the variance is ${{4}\over{9}}$ The mean is $2$ and the variance is $16$ The mean is $8$ and the variance is $16$ The mean is $2$ and the variance is ${{16}\over{25}}$ The mean is $2$ and the variance is ${{4}\over{9}}$

  5. An actual voltage of new battery has the mean value of $3$ and the variance ${{1}\over{3}}$. Consider the average voltage $Y$ of $3$ new batteries. Approximate $P( {{5}\over{2}} < Y < {{7}\over{2}})$.

    $\Phi( {{3}\over{2}}) - \Phi( -{{3}\over{2}}) \approx 0.8664$ $\Phi( {{1}\over{3}}) - \Phi( -{{1}\over{3}}) \approx 0.2611$ $\Phi( 1) - \Phi( -1) \approx 0.6827$ $\Phi( {{1}\over{2}}) - \Phi( -{{1}\over{2}}) \approx 0.3829$


Department of Mathematics
Last modified: 2026-10-28