Question

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%

Answer #1

Let H be the number of heads in 400 tosses of a fair coin. Find
normal approximations to:
a) P(190 < H < 210)
b) P(210 < H < 220)
c) P(H = 200)
d) P(H=210)

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

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

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?

A fair coin is flipped 30 times. If X = the number of H s, then
the approximate value of P(X = 15) is..
a) .074
b) .193
c) .097
d) .146

Suppose a coin is randomly tossed n = 400 times, resulting in X
= 240 Heads. Answer each of the following; show all work!
(a) Calculate the point estimate, and the corresponding
two-sided 95% confidence interval, for the true probability pi =
P(Heads), based on this sample.
(b) Calculate the two-sided 95% acceptance region for the null
hypothesis H0: pi = 0.5 that the coin is fair.
(c) Calculate the two-sided p-value (without correction term) of
this sample, under the...

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).

consider a coin with P(head) =0.45 and P(tail)=0.55. the coin is
flipped 1000 times. let X be the number of heads obtained .using
chebyshev's inequality, find a lower bound for P(30<X<60)

A coin is tossed five times. Let X = the number of heads. Find
P(X = 3).

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

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