Question

a
fair coin is flipped 44 times. let X be the number if heads. what
normal distribution best approximates X?

Answer #1

n = Number of trials = 44

p = Probability of success = 0.5

q= Probability of failure = 1 - 0.5 = 0.5

Mean = np = 44 X 0.5 = 22

SD =

Conditions for Normal approximation to Binomial are satisfied as follows:

np = 40 X 0.5 = 22 >5

and

n(1- p) = 44 X (1 - 05) = 22> 5

So,

Normal distribution that best approximates X is as follows:

**Normal Distribution with mean = =
22 and SD =
= 3.3166**

A fair coin is flipped 400 times. Let X be the number of heads
resulting, find P[190<= X <= 200]
a) About 34%
b) About 95%
c) About 68%
d) About 25%
e) About 50%

As in the previous problem, a fair coin is flipped 28 times. If
X is the number of heads, then the distribution of X can be
approximated with a normal distribution, N(14,2.6), where the mean
(μ) is 14 and standard deviation (σ) is 2.6. Using this
approximation, find the probability of flipping 18 or 19 heads. You
may use the portion of the Standard Normal Table below.
z1.21.31.41.51.61.71.81.92.02.12.20.000.88490.90320.91920.93320.94520.95540.96410.97130.97720.98210.98610.010.88690.90490.92070.93450.94630.95640.96490.97190.97780.98260.98640.020.88880.90660.92220.93570.94740.95730.96560.97260.97830.98300.98680.030.89070.90820.92360.93700.94840.95820.96640.97320.97880.98340.98710.040.89250.90990.92510.93820.94950.95910.96710.97380.97930.98380.98750.050.89440.91150.92650.93940.95050.95990.96780.97440.97980.98420.98780.060.89620.91310.92790.94060.95150.96080.96860.97500.98030.98460.98810.070.89800.91470.92920.94180.95250.96160.96930.97560.98080.98500.98840.080.89970.91620.93060.94290.95350.96250.96990.97610.98120.98540.98870.090.90150.91770.93190.94410.95450.96330.97060.97670.98170.98570.9890

If a fair coin is flipped 120 times, what is the probability
that:
The number of heads is more than 70
The number of heads between 50 and 70?

PROBLEM 4. Toss a fair coin 5 times, and let X be the number of
Heads. Find P ( X=4 | X>= 4 ).

A coin is flipped three times; give the probability distribution
of the number of heads.

Suppose a fair coin (P[heads] = ½) is flipped 50 times. What is
the probability of obtaining 30 or fewer heads using the normal
approximation to the binomial with the continuity correction
factor?
Use Minitab or some other software package to obtain the your
probability answer. Round your answer to two decimal points.

A fair coin has been tossed four times. Let X be the number of
heads minus the number of tails (out of four tosses). Find the
probability mass function of X. Sketch the graph of the probability
mass function and the distribution function, Find E[X] and
Var(X).

Toss a fair coin for three times and let X be the number of
heads.
(a) (4 points) Write down the pmf of X. (hint: first list all
the possible values that X can take, then calculate the probability
for X taking each value.)
(b) (4 points) Write down the cdf of X.
(c) (2 points) What is the probability that at least 2 heads
show up?

When a fair coin is flipped N times, the average number of heads
<n> , is N/2 and, in any particular trail, the “fluctuation”
about this average, the standard deviation (variance), is expected
to be sigma = sqrt(<n^2>-,<n>^2) . Calculate the
probability that for N=16 the number of heads in one trail will be
outside the expected range N/2+ sigma to N/2- sigma

suppose i flip a coin n=100 times and i obtain heads x=44 times.
assuming the coin is fair, calculate P(x>44) using the normal
approximation with continuity correction. x=44 significantly
low

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