Question

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.

Answer #1

Let X is a random variable shows the number of heads out of 50. Here X has binomial distribution with parameter n=50 and p=1/2 = 0.50.

Since np = 25 and n(1-p) = 25 both are greater than 5 so we can use normal approximation here.

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

Using continuity correction factor we have

The z-score for X = 30.5 is

The probability of obtaining 30 or fewer heads using the normal approximation to the binomial with the continuity correction factor is

Excel function used: "=NORMSDIST(1.56)"

**Answer: 0.94**

Find the probability of more than 30 heads in 50 flips of a fair
coin by using the normal approximation to the binomial
distribution.
a) Check the possibility to meet the requirements to use normal
approximation (show your calculation)
b) Find the normal parameters of the mean(Mu) and standard
deviation from the binomial distribution.
c) Apply normal approximation by using P(X>30.5) with
continuity correction and find the probability from the table of
standard normal distribution.

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

Suppose a fair coin is flipped three times.
A). What is the probability that the second flip is heads?
B). What is the probability that there is at least two
tails?
C). What is the probability that there is at most two heads?

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?

Given a fair coin, if the coin is flipped n times, what is the
probability that heads is only tossed on odd numbered tosses.
(tails could also be tossed on odd numbered tosses)

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

A
coin is flipped 15 times. find the probability of the following:
p( exactly 4 Heads).
p( at most 2 Heads).
p( at least 3 Heads).
please explain. Thanks

A fair coin is flipped six times. Find the probability that
heads comes up exactly four times.
1/16
15/64
90/16
1/4
2/3

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

A coin is flipped 12 times. Using the normal approximation of
the binomial distribution, calculate the probability of observing
either 6, 7, or 8 heads.

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