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# This homework covers some counting and probability problems, binomial and normal distrtut,on problems

INSTRUCTIONS TO CANDIDATES
###### ANSWER ALL QUESTIONS

This homework covers some counting and probability problems, binomial and normal distrtut,on

problems and simulations with the Central Limit Theorem Irons module 2. You are allowed to work

together, but are expected to submit your own answers. Please slow work where appropriate,

including snippets/graphics Iron IMP output. In general, the correct answer will suffice, but any work

can assist in partial credit should your answer to a question be wrong. Otherwise it wil be difficult for

me to determin, what you may have been trying to do You should wbmit either a word or pdf

document with your answers to each question. You should name your submission to this homework

lastname_hwi.doc (or docs for more recent word versions) or laslname_hwl.pdf,

1. There are S red. 11 yellow, and 4 green balls in a bag You will randomly draw 2 from the bag.

a What lithe sample space for this experiment (al possible outcomes of drawing 2 bals

from this bag, you may consider the order In which they are drawn. Le. red/yellow Ii

different than yellow/red)?

b. What is the probability that you draw 2 yellow balls from the bag? This is done without

repLacement (that Is, once you draw the first bal, there s one fewer in the bag for the

second draw).

c Create a table for the probablhty distrdutlon for this experiment (probability for each

event ‘n your answer to a).

2. You flip an unfair coin 4 times which has P(Heads) 06 and P(Tails) 0.4. You are interested in

counùrw how many times the coin lands Heath. Create a probability distribution for this

expenment. 8e sure that your probatidity distribution shows the correct outcomes (possibilities of

how many Heads you could get In flipping 4 coins).

3. At Denver International Airport, each ir rmtirig plane has an 84% chance of landing on time. A

sample of IS flights ‘s studled Assasie eicts flight’s arrival rs .dependent of one another

a. Can the binomial d,stnbution be used here? If so, why? (check the assumptions)

b. How many Ihghts would you expect to land on time (that Is. what Is the mean 04 thIs

distnbution).

c.. Find the probability that all 15 flights arrive on time.

d. Find the probability that 13 flights arrive on time

e. Find the probability that 13 or fewer flights arrive on time.

f Find the probability that 11 or more flights arrive on time,

4. The blowing require you to find areas under the standard normal curve

a. Find the area under the standard normal curve that lies between z. -1 and z  0.5

b. Find the area under the standard normal curve that lles to the right of z 2.

c. Find the area under the standard normal curve that lles to the left of z. •1 .2

5. FInd the ¿score for which:

a. The area to its left is 0.04

b. The area to its left is 0.7

C. The area toits right s 0.4

d. The area to its right s 08

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