PSY 555 Homework 9

Answers

5.14.
p(that
any applicant will be admitted)=the ratio of the number admitted to the number
applying=10/300=.03.

There
is a _{} probability that a
person in the top 20% will be admitted using this procedure.

5.21. Plot
of correct choices on trial 1 of a 5-choice task.

5.23.
p(5 or
more correct)=p(5)+p(6)+p(7)+p(8)+p(9)+p(10)
=.0264+.0055+.0008+.0001+.0000+.0000=.028_{}.

Assuming
that the alpha level we use is equal to .05, four choices (with a probability
of .0881) still falls within chance levels.
The probability of five people making correct choices is .028, which
falls below the .05 alpha level. So, it
is relatively safe to conclude that five correct choices for the first trial
indicates subjects are performing above chance levels.

5.26.
Number
of subjects needed in verbal learning experiment if each is to see different
classes of words in a different order.

_{}

We
would need 24 subjects—1 for each of the 24 possible permutations.

5.29.
The
total number of ways of making ice cream cones=

_{}

They
can truthfully advertise that they have 63 different combinations.

5.30.
Different
ways to record from the rat’s brain:

_{}

There
are 15 ways to record from the brain.

1.
Permutations
are all the possible orderings of variable elements.

_{}

An
example of a permutation would be trying to decide all the permutations of 4
posters to displayed on a museum wall, if only two posters can be on the wall
at any given time.

AB
BA

AC
CA

AD
DA

BC
CD

BD
DB

CD
DC

Combinations
are all the possible different pairings of variable elements (order does not
matter for these).

An
example of a combination would be the pairings of food for dinner plates at a
buffet with 4 different types of food, if on each dinner plate you get to
choose 3 items(assuming you don’t care what food is touching, i.e., order
doesn’t matter).

Chicken,corn,potatoes

Apple,potatoes,corn

Corn,apple,chicken

Chicken,potatoes,apple

2. N=10

r=7

_{}

There
are 604,800 possible passwords he will need to try.

3. Need to use the binomial distribution formula for this
problem (0 to 3 plus 17 to 20)

4(a). The
answer depends on how you interpreted the question. If you interpreted it as one of the first four
cards that the dealer receives being a red joker, the probability is calculated
as follows:

P[joker
on first draw)=_{}

P[joker
on second draw)=_{}

P[joker
on third draw)=_{}

P{joker
on fourth draw)=_{}

P[J+J+J+J]=_{}

There
is a .00000001334 probability that the first four cards that the dealer
receives will all be red jokers.

If
you interpreted the problem to mean the probability that all of the first four
cards dealt out by the dealer being a red joker, then the probability is
calculated as follows:

P[joker
on first draw)=_{}

P[joker
on second draw)=_{}

P[joker
on third draw)=_{}

P{joker
on fourth draw)=_{}

P[J+J+J+J]=_{}

There
is a .00000001134 probability that the first four cards that are dealt by the
dealer will all be red jokers.

4(b). The
answer depends on how you interpreted the question. If you interpreted it as one of the first
five cards that the dealer receives being a red joker, the probability is
calculated as follows:

P[joker
on first draw)=_{}

P[joker
on second draw)=_{}

P[joker
on third draw)=_{}

P{joker
on fourth draw)=_{}

P(joker
on fifth draw)=_{}

P[J
or J or J or J or J]=_{}

There
is a .0981 probability that one of the dealer's first five cards drawn will be
a red joker.

If
you interpreted the problem to mean the probability that one of the first five
cards dealt out by the dealer being a red joker, then the probability is
calculated as follows:

P[joker
on first draw)=_{}

P[joker
on second draw)=_{}

P[joker
on third draw)=_{}

P{joker
on fourth draw)=_{}

P(joker
on fifth draw)=_{}

P[J
or J or J or J or J]=_{}

There
is a .0935 probability that one of the first five cards dealt will be a red
joker.

4(c). The
probability is 0 that each person will start the game with a red joker because
there are five people and only four red jokers in the deck.

4(d). Player
1—A,K,2,6,8,10,Jack

Player 2-Red Joker,9,3,5,4,Jack, Black Joker

Player 3-K,Q,3,6,9,10,Black Joker

Player 4-2,7,7,10,Q,K,A

Player 5-4,8,8,Jack,Red Joker,Q,7

Given
this information, what is the probability that the next card drawn from the
deck will be a 4?

216-35=181
card left in the deck

(4
fours)(4 decks)=16[4's]-2[4's]=Fourteen 4's left in the deck

P[4]=_{}

There
is a .0773 probability that the next card drawn from the deck will be a 4.