Generating...                               quiz02_n29

  1. Let $Z$ be a standard normal random variable. Find the value of $x$ such that $P(Z > x) = 0.01$.

    $1.16$ $2.33$ $1.28$ $0.64$

  2. 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 $n = 25$ seeds is between 17.7 and 20.9 days.

    $\Phi( 2.42) - \Phi( -0.25) \approx 0.5909$ $\Phi( 2.4) - \Phi( -0.8) \approx 0.7799$ $\Phi( 2.0) - \Phi( -0.67) \approx 0.7248$ $\Phi( 2.9) - \Phi( -0.3) \approx 0.616$

  3. Consider a sample $X_1,\ldots,X_{ 16}$ of normally distributed random variables with mean $\mu = 1$ and variance $\sigma^2 = 4$. What is the probability that $0.6 \le \bar{X} \le 1.4$?

    $\Phi( 0.1) - \Phi( -0.1) \approx 0.0797$ $\Phi( 1.6) - \Phi( -1.6) \approx 0.8904$ $\Phi( 0.4) - \Phi( -0.4) \approx 0.3108$ $\Phi( 0.2) - \Phi( -0.2) \approx 0.1585$ $\Phi( 0.8) - \Phi( -0.8) \approx 0.5763$

  4. An actual voltage of new battery has the mean value of $6$ and the variance ${{1}\over{3}}$. Consider the the average voltages from 20 new batteries. Find the mean and the variance.

    The mean is $6$ and the variance is ${{1}\over{60}}$ The mean is ${{3}\over{10}}$ and the variance is ${{1}\over{60}}$ The mean is $6$ and the variance is $20$ The mean is ${{3}\over{10}}$ and the variance is $20$ The mean is $6$ and the variance is ${{1}\over{20}}$ The mean is ${{3}\over{10}}$ and the variance is ${{1}\over{20}}$

  5. An actual voltage of new battery has the mean value of $6$ and the variance ${{1}\over{3}}$. Consider the average voltage $Y$ of $12$ new batteries. Approximate $P( {{17}\over{3}} < Y < {{19}\over{3}})$.

    $\Phi( {{3}\over{2}}) - \Phi( -{{3}\over{2}}) \approx 0.8664$ $\Phi( {{1}\over{4}}) - \Phi( -{{1}\over{4}}) \approx 0.1974$ $\Phi( 2) - \Phi( -2) \approx 0.9545$ $\Phi( {{1}\over{3}}) - \Phi( -{{1}\over{3}}) \approx 0.2611$


Department of Mathematics
Last modified: 2026-05-20