Question: Suppose that a fair coin is tossed 290 times with the results of the tosses regarded as independent events. Use the central limit theorem to approximate the probability that the total number of heads obtained is greater than 147.
Question: Suppose that a fair coin is tossed 290 times with the results of the tosses regarded as independent events. Use the central limit theorem to approximate the probability that the total number of heads obtained is greater than 147.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![The central limit theorem states that if
Y1, Y2, ... , Yn
are a sequence of random variables that are independent and identically distributed
with
E[Y;] = µ
V[Y;] = o²
for each i (with both of those quantities being finite), and
n
1
Yn
n
i=
is the sample mean random variable, when n is large, we can approximate the
distribution of the sample mean as
Yn - Normal(u, o²In)
and also approximate the distribution of the sum
n
S, = EY;
Σ
i=1
as
S, ~ Normal(nµ, no²).
Question: Suppose that a fair coin is tossed 290 times with the results of the tosses
regarded as independent events. Use the central limit theorem to approximate the
probability that the total number of heads obtained is greater than 147.
• use the Normal probability tables to look up the probability
• the table can be used for arguments specified up to 2 decimal places, so
round your argument appropriately
• do not use a continuity correction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F916ef916-4947-4ac0-96f9-f8ffb94d15c0%2Fd668d1f1-0ba1-4042-9044-98403a506eb7%2Fm7j9o08_processed.png&w=3840&q=75)
Transcribed Image Text:The central limit theorem states that if
Y1, Y2, ... , Yn
are a sequence of random variables that are independent and identically distributed
with
E[Y;] = µ
V[Y;] = o²
for each i (with both of those quantities being finite), and
n
1
Yn
n
i=
is the sample mean random variable, when n is large, we can approximate the
distribution of the sample mean as
Yn - Normal(u, o²In)
and also approximate the distribution of the sum
n
S, = EY;
Σ
i=1
as
S, ~ Normal(nµ, no²).
Question: Suppose that a fair coin is tossed 290 times with the results of the tosses
regarded as independent events. Use the central limit theorem to approximate the
probability that the total number of heads obtained is greater than 147.
• use the Normal probability tables to look up the probability
• the table can be used for arguments specified up to 2 decimal places, so
round your argument appropriately
• do not use a continuity correction.
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