Exercise Set 17

  1. A normally distributed random variable \(X\) has mean \(1\) and variance \(4\). Using tables, find

    1. \(P(X>0)\)
    2. \(P(X<2)\)
    3. \(P(|X|<1)\)
    4. the value of \(c\) such that \(P(X<c)=0.0643\)

  2. A normally distributed random variable \(X\) has mean 1 and variance 5. Using tables, find:

    1. \(P(X > 1)\)
    2. \(P(|X| < 0.1)\)
    3. The value of \(c\) such that \(P(X < c) = 0.01287\)

  3. A thermostat is set to switch at \(20^\circ\,\text{C}\) operates in a range of temperatures with a mean value of \(20.4^\circ\,\text{C}\) and a standard deviation of \(1.3^\circ\,\text{C}\). What is the probability that its operating temperature will fall between \(19.5^\circ\,\text{C}\) and \(20.5^\circ\,\text{C}\)?

  4. The life of a drill has a mean of 16 hours and a standard deviation of 2.6 hours. Assuming it is normally distributed determine the probability of a bit lasting

    1. More than 20 hours.
    2. Less than 14 hours.