Statistics for laboratory scientists

Homework problems for lecture 9

  1. Suppose X ~ normal(mean=5, SD=3). Calculate the following. (Try these both using R and a table.)

    1. Pr(X < 6)

    2. Pr(X > 0)

    3. Pr(0 < X < 5)

    4. Pr(2 < X < 8)

    5. Pr(|X - 5| > 2)

  2. Suppose Y ~ normal(mean=200, SD=18). Calculate the following. (Again, try these both using R and a table.)

    1. Pr(Y > 250)

    2. Pr(180 < Y < 220)

    3. Pr(|Y - 180| > 20)

  3. [problem 6.3 in Sokal & Rohlf, pg 125] Assume that the petal length of a population of plants of species X is normally distributed with mean=3.2cm and SD=0.8cm. What proportion of the population would be expected to have a petal length:

    1. Greater than 4.5cm?

    2. Greater than 1.78cm?

    3. Between 2.9 and 3.6cm?

  4. Suppose X and Y are independent, X ~ binomial(n=5, p=0.1), and Y ~ binomial(n=5, p=0.4). Calculate the following.

    1. E(X+Y)

    2. SD(X+Y)

    3. E[(X+Y)/2]

    4. SD[(X+Y)/2]

    5. E(X - Y)

    6. SD(X - Y)

  5. Suppose X1, X2, X3, ..., X10 are independent and identically distributed (iid), with mean=3 and SD=3. Calculate the following.

    1. E(X1 + X2 + ... + X10)

    2. SD(X1 + X2 + ... + X10)

    3. E[(X1 + X2 + ... + X10)/10]

    4. SD[(X1 + X2 + ... + X10)/10]


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Last modified: Wed Feb 22 09:44:03 EST 2006