If a symmetric coin is tossed 100 times, by using normal
approximation find the probability that:
a. it comes up H more than 60 times
b. the number of H(X) is between 60 and 90 (60≤X≤90)
A coin is tossed 279 times. Use either a Normal or Poisson
approximation to approximate the probability that there are at most
43 heads. Show that the approximation is applicable and use the
Padé approximation to determine the result.
DO NOT USE!!!! TI-83, TI-84, TI-89 NOR Excel commands for the
Binomial distribution to determine the result.
Assume we flip a fair coin 100 times. Use the normal
approximation to the binomial distribution to approximate the
probability of getting more than 60 heads.
Answer: 0.0108 - need work
A fair coin is tossed two times, and the events A and B are
defined as shown below. Complete parts a through d.
A: {At most one tail is observed}
B: {The number of tails observed is even}
a. Identify the sample points in the events A, B, AunionB,
Upper A Superscript c, and AintersectB.
Identify the sample points in the event A. Choose the correct
answer below.
A. A:{TT comma HH}
B. A:{TT}
C. A:{HH comma HT comma TH}...
A fair coin will be tossed three times.
(a) Indicating a head by H and a tail by T write down the
outcome space.
(b) What is the probability that on the first toss the outcome
with a tail?
(c) What is the probability of obtaining exactly two heads from
the three coin tosses?
(d) What is the probability that the first toss gives a tail and
exactly two heads are obtained from the three coin tosses? Are the
outcomes...
If a fair coin is tossed 25 times, the probability distribution
for the number of heads, X, is given below. Find the mean and the
standard deviation of the probability distribution using Excel
Enter the mean and round the standard deviation to two decimal
places.
x P(x)
0 0
1 0
2 0
3 0.0001
4 0.0004
5 0.0016
6 0.0053
7 0.0143
8 0.0322
9 0.0609
10 0.0974
11 0.1328
12 0.155
13 0.155
14 0.1328
15 0.0974
16 ...
A fair coin is tossed r times. Let Y be the number of heads in
these r tosses. Assuming Y=y, we generate a Poisson random variable
X with mean y. Find the variance of X. (Answer should be based on
r).
A fair coin is tossed 100 times. What is the probability of
observing at least 55 heads P(x≥55)? (Approximate the binomial
distribution with a normal distribution
A fair coin is tossed 4 times.
a. Write the outcomes of the sample space
b. Let A be the event of obtaining at least one head, find
P(A)
c. Let B be the event of obtaining at least one tail, find
P(B)
d. Let C be the event of obtaining two tails, find P(C)
e. Find P(A ∪ B)
f. Find P(A ∩ B)
g. Find P(A ∪ B ∪ C)