Generating...                               quiz02_n12

  1. An actual voltage of new battery has the mean value of $6$ and the variance ${{4}\over{3}}$. Consider the the average voltages from 30 new batteries. Find the mean and the variance.

    The mean is $6$ and the variance is ${{1}\over{30}}$ The mean is $6$ and the variance is $30$ The mean is ${{1}\over{5}}$ and the variance is ${{2}\over{45}}$ The mean is ${{1}\over{5}}$ and the variance is $30$ The mean is ${{1}\over{5}}$ and the variance is ${{1}\over{30}}$ The mean is $6$ and the variance is ${{2}\over{45}}$

  2. An actual voltage of new battery has the mean value of $9$ and the variance ${{1}\over{3}}$. Consider the average voltage $Y$ of $27$ new batteries. Approximate $P( {{26}\over{3}} < Y < {{28}\over{3}})$.

    $\Phi( {{1}\over{4}}) - \Phi( -{{1}\over{4}}) \approx 0.1974$ $\Phi( {{1}\over{3}}) - \Phi( -{{1}\over{3}}) \approx 0.2611$ $\Phi( {{9}\over{4}}) - \Phi( -{{9}\over{4}}) \approx 0.9756$ $\Phi( 3) - \Phi( -3) \approx 0.9973$

  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 $n = 36$ seeds is between 17.9 and 20.6 days.

    $\Phi( 2.6) - \Phi( -0.1) \approx 0.5352$ $\Phi( 3.83) - \Phi( -0.67) \approx 0.7474$ $\Phi( 4.33) - \Phi( -0.17) \approx 0.5662$ $\Phi( 2.3) - \Phi( -0.4) \approx 0.6447$

  4. 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, find the mean and the variance for the average germination time $\bar{X}$ of $n = 100$ seeds.

    The mean is $18$ and the variance is $1$ The mean is $18$ and the variance is $36$ The mean is ${{9}\over{2}}$ and the variance is $36$ The mean is $18$ and the variance is ${{9}\over{25}}$ The mean is ${{9}\over{2}}$ and the variance is ${{9}\over{25}}$ The mean is ${{9}\over{2}}$ and the variance is $1$

  5. Let $X$ be a normal random variable with $\mu = 6$ and $\sigma = 10$. Find $P(X > 20)$.

    $0.758$ $1 - 0.8849$ $0.8849$ $0.9192$ $1 - 0.9192$ $1 - 0.758$


Department of Mathematics
Last modified: 2026-03-24