Generating...                               quiz02_n4

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

  2. An actual voltage of new battery has the mean value of $6$ and the variance ${{1}\over{3}}$. Consider the average voltage $Y$ of $27$ new batteries. Approximate $P( {{17}\over{3}} < Y < {{19}\over{3}})$.

    $\Phi( {{1}\over{2}}) - \Phi( -{{1}\over{2}}) \approx 0.3829$ $\Phi( {{9}\over{2}}) - \Phi( -{{9}\over{2}}) \approx 1.0$ $\Phi( {{1}\over{3}}) - \Phi( -{{1}\over{3}}) \approx 0.2611$ $\Phi( 3) - \Phi( -3) \approx 0.9973$

  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 $n = 100$ seeds is between 1.8 and 2.2 days.

    $\Phi( 0.0) - \Phi( -2.0) \approx 0.4772$ $\Phi( 0.5) - \Phi( -0.5) \approx 0.3829$ $\Phi( 0.0) - \Phi( -1.0) \approx 0.3413$ $\Phi( 1.0) - \Phi( -1.0) \approx 0.6827$

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

    $0.9452 - 0.7257 = 0.2195$ $0.8849 - 0.5793 = 0.3057$ $0.7881 - 0.6179 = 0.1702$ $0.7257 - 0.5398 = 0.1859$

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

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


Department of Mathematics
Last modified: 2025-10-30