Generating...                               quiz02_n13

  1. An actual voltage of new battery has the mean value of $9$ and the variance ${{1}\over{3}}$. Consider the average voltage $Y$ of $12$ new batteries. Approximate $P( {{26}\over{3}} < Y < {{28}\over{3}})$.

    $\Phi( 3) - \Phi( -3) \approx 0.9973$ $\Phi( {{1}\over{3}}) - \Phi( -{{1}\over{3}}) \approx 0.2611$ $\Phi( 2) - \Phi( -2) \approx 0.9545$ $\Phi( {{1}\over{2}}) - \Phi( -{{1}\over{2}}) \approx 0.3829$

  2. Let $X$ be a normal random variable with $\mu = 8$ and $\sigma = 5$. Find $P( -10 < X < 0)$.

    $0.3085 - 0.1587 = 0.1499$ $0.0548 - 2.0 \times 10^{-4} = 0.0546$ $0.0228 - 0.0 = 0.0227$ $0.3446 - 0.1841 = 0.1605$

  3. The germination time in days of a newly planted seed has the mean value of $18$ and variance $36$. If the germination times $X_1,\ldots,X_n$ are independent, estimate the probability that the average germination time $\bar{X}$ of $n = 100$ seeds is between 18.6 and 19.7 days.

    $\Phi( 2.83) - \Phi( 1.0) \approx 0.1564$ $\Phi( 0.92) - \Phi( 0.0) \approx 0.3203$ $\Phi( 1.83) - \Phi( 0.0) \approx 0.4666$ $\Phi( 1.42) - \Phi( 0.5) \approx 0.2302$

  4. Let $Z$ be a standard normal random variable. Find the value of $x$ such that $P(Z > x) = 0.1$.

    $1.28$ $2.56$ $4.66$ $2.33$

  5. 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 $n = 100$ seeds.

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


Department of Mathematics
Last modified: 2025-09-14