Generating...                               quiz02_n21

  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 20 new batteries. Find the mean and the variance.

    The mean is $6$ and the variance is ${{1}\over{15}}$ The mean is ${{3}\over{10}}$ and the variance is $20$ The mean is ${{3}\over{10}}$ and the variance is ${{1}\over{20}}$ The mean is ${{3}\over{10}}$ and the variance is ${{1}\over{15}}$ The mean is $6$ and the variance is $20$ The mean is $6$ and the variance is ${{1}\over{20}}$

  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 $P( {{26}\over{3}} < Y < {{28}\over{3}})$.

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

  3. 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, estimate the probability that the average germination time $\bar{X}$ of $n = 25$ seeds is between 7.5 and 8.9 days.

    $\Phi( 1.35) - \Phi( -0.75) \approx 0.6849$ $\Phi( 0.71) - \Phi( -1.04) \approx 0.6118$ $\Phi( 1.13) - \Phi( -0.62) \approx 0.6037$ $\Phi( 0.85) - \Phi( -1.25) \approx 0.6967$

  4. Consider a sample $X_1,\ldots,X_{ 9}$ of normally distributed random variables with mean $\mu = 2$ and variance $\sigma^2 = 0.25$. What is the probability that $1.7 \le \bar{X} \le 2.3$?

    $\Phi( 1.8) - \Phi( -1.8) \approx 0.9281$ $\Phi( 0.3) - \Phi( -0.3) \approx 0.2358$ $\Phi( 0.1) - \Phi( -0.1) \approx 0.0797$ $\Phi( 1.2) - \Phi( -1.2) \approx 0.7699$ $\Phi( 0.45) - \Phi( -0.45) \approx 0.3473$

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

    $1.28$ $3.28$ $2.56$ $1.64$


Department of Mathematics
Last modified: 2026-09-10