6
The Binomial Distribution (and Other Discrete Distributions)
6.1
The Binomial Probability Distribution and Theoretical Frequency
Distribution
6.2
Probability Distributions and Theoretical Frequency Distributions in
General
6.3
The Mean and Standard Deviation of a Binomial Distribution
6.4
Histogram of a Binomial Distribution
EXERCISES
1. (a) Find the binomial distribution obtained by rolling 6 dice, considering a
1 a success and everything else a failure.
(b) Find the theoretical frequency distribution, if these 6 dice are rolled
46,656 times.
(c) Construct the histogram for part (b).
2. Five coins are tossed 64 times.
(a) Construct the theoretical frequency table for 0, 1, ..., 5 heads.
(b) Draw the corresponding histogram.
(c) Find the expected number of times of getting at least 3 heads.
(d) In the histogram, shade the area that is a measure of the result in part
(c).
(e) Toss 5 coins 64 times and record the actual frequencies of 0, 1,..., 5
heads.
(f) Calculate the mean and standard deviation of the frequency distribution
obtained in part (a) by use of Formulae (6-6) and (6-7), as was done in Table 69.
(g) Calculate the mean and standard deviation of part (f) by use of Theorem 6-2.
(h) Calculate the mean and standard deviation of the observed frequency
distribution obtained in part (e).
(i)
Draw the histogram of the observed frequency distribution on the same page
the histogram of the theoretical frequency distribution in part (b) was drawn
on.
3. If 5 coins are tossed 3000 times, answer the same questions asked in Exercise
2(a), (b), (c), (d), (f), and (g).
4. Four dice are rolled 81 times.
everything else a failure
If a 1 or a 6 is considered a success and
(a) construct the theoretical frequency table for 0, 1, 2, 3, 4 successes;
(b) draw the corresponding histogram;
(c) find the expected number of times of obtaining at least 3 successes among
the 4 dice.
(d) In the histogram, shade the area that is a measure of the result in part
(c).
(e) Roll 4 dice 81 times and record the actual frequencies for 0, 1, 2, 3, 4
successes.
(f) Calculate the mean and standard deviation of the frequency distribution
obtained in part (a) by use of Formulae (6-6) and (6-7), as was done in Table 69.
(g) Calculate the mean and standard deviation of part (f) by use of Theorem 6-2.
5. (a) Find the theoretical binomial frequency distribution with n = 5, p = 0.7,
and N = 90.
(b) Find its mean and standard deviation.
(c) Compare the theoretical frequencies obtained in part (a) with the actual
ones given in Table 6-11.
1AAEC 3401
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