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Statistical Probabilities and Distributions
Homework for Prob./Dist. Lesson 9
- Separately calculate using the binomial formula
the probabilities of getting 0, 1, 2, 3, or 4
left-handed students in a class of 25, given a probability of 0.1.
Compare your results with those obtained by doing binompdf(25,.1)
(DISTR 0) or running BINOMIAL on your TI-83+ graphing calculator.
- Using only the data from the problem above, and the data from the
example in the lecture, find the probability of getting
more than four left-handed students in a class of 25.
Compare your results with those obtained by doing
1-binomcdf(25,.1) (DISTR A) on your TI-83+ graphing calculator.
- Check the assumptions carefully and see if we are justified in
using the binomial (and not the hypergeometric) distribution
for the problems above.
- Calculate the probability described in the text for winning the
lottery by matching all 6 of 54 numbers.
- Calculate the probability described in the text for winning the
lottery by matching 5 of the 6 selected numbers from 54.
- Calculate the probability described in the text for losing the
lottery by not matching any of the 6 selected numbers from 54.
- Use the normal approximation for the binomial to calculate
the probability of getting 11 heads in 20 attempts from a fair coin
(ignore the magic number test).
Be sure to use the continuity correction and calculate the
area under the probability density curve from 10.5 to 11.5.
Compare this carefully with the results from the binomial formula.
- Use the normal approximation for the binomial to calculate
the probability of getting 12 heads in 20 attempts from a fair coin
(ignore the magic number test).
Compare this carefully with the results from the binomial formula.
Is this the same as the probability of getting 8 heads?
- Use the normal approximation for the binomial to calculate
the probability of getting 13 heads in 20 attempts
(ignore the magic number test).
Compare this carefully with the results from the binomial formula.
Is this the same as the probability of getting 7 heads?
- How likely is it to get 15 or more heads in 20 attempts,
if the coin is fair?
- A common rule is that you can approximate the binomial
with the normal when both ?.....? and ?.....? exceed the magic
number of ?.....?.