Question

**Fair Coin?** A coin is called *fair* if it
lands on heads 50% of all possible tosses. You flip a game token
100 times and it comes up heads 42 times. You suspect this token
may not be *fair*.

(a) What is the point estimate for the proportion of heads in
all flips of this token? **Round your answer to 2 decimal
places.**

(b) What is the critical value of *z* (denoted
*z*_{α/2}) for a 99% confidence interval?
**Use the value from the table or, if using software, round
to 2 decimal places.**

*z*_{α/2} =

(c) What is the margin of error (*E*) for a 99% confidence
interval? **Round your answer to 3 decimal
places.**

*E* =

(d) Construct the 99% confidence interval for the proportion of
heads in all tosses of this token. **Round your answers to 3
decimal places.**

< *p* <

(e) Are you 99% confident that this token is **not**
fair?

No, because 0.50 is within the confidence interval limits.Yes,
because 0.50 is **not** within the confidence interval
limits. Yes, because 0.50 is within the
confidence interval limits.No, because 0.50 is **not**
within the confidence interval limits.

Answer #1

Fair Coin? A coin is called fair if it lands on heads 50% of all
possible tosses. You flip a game token 100 times and it comes up
heads 60 times. You suspect this token may not be fair.
(a) What is the point estimate for the proportion of heads in
all flips of this token? Round your answer to 2 decimal places.
(b) Construct the 99% confidence interval for the proportion of
heads in all tosses of this token....

A coin is called fair if it lands on heads 50% of all possible
tosses. You flip a game token 100 times and it comes up heads 61
times. You suspect this token may not be fair. (a) What is the
point estimate for the proportion of heads in all flips of this
token? Round your answer to 2 decimal places. (b) What is the
critical value of z (denoted zα/2) for a 90% confidence interval?
Use the value from...

Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.39. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.04 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...

You flip a fair coin. If the coin lands heads, you roll a fair
six-sided die 100 times. If the coin lands tails, you roll the die
101 times. Let X be 1 if the coin lands heads and 0 if the coin
lands tails. Let Y be the total number of times that you roll a 6.
Find P (X=1|Y =15) /P (X=0|Y =15) .

Suppose you flip a fair coin until it lands heads up for the
first time. It can be shown (do not try to calculate this) that the
expected value of the number of flips required is 2. Explain (with
a sentence or two) what this expected value means in this
context.

When coin 1 is flipped, it lands on heads with probability
3/5 ; when coin 2 is flipped it lands on heads with probability
4/5 .
(a)
If coin 1 is flipped 12 times, find the probability that it
lands on heads at least 10 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the first of...

When coin 1 is flipped, it lands on heads with probability
3
5
; when coin 2 is flipped it lands on heads with probability
4
5
.
(a)
If coin 1 is flipped 11 times, find the probability that it
lands on heads at least 9 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the...

A fair coin is tossed 4 times, what is the probability
that it lands on Heads each time?

The theoretical probability of a coin landing heads up is
1/2
Does this probability mean that if a coin is flipped two times,
one flip will land heads up? If not, what does it mean?
Choose the correct answer below.
A.
Yes, it means that if a coin was flipped two times, at least
one of the tosses would land heads up.
B.
Yes, it means that if a coin was flipped two times, exactly
one of the tosses would...

Question 3: You are
given a fair coin. You flip this coin twice; the two flips are
independent. For each heads, you win 3 dollars, whereas for each
tails, you lose 2 dollars. Consider the random variable
X = the amount of money that you
win.
– Use the definition of expected value
to determine E(X).
– Use the linearity of expectation to
determineE(X).
You flip this coin 99 times; these
flips are mutually independent. For each heads, you win...

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