For n successive Bernoulli trials with probability p of success on each trial, the mean number of successes u is given by u= np, and the standard deviation for the number of successes is given by o = /np(1-p). Use this formula to solve the following problem. A fair coin is tossed 64 times. We know that the mean number of times heads appears is p=np = (64)(0.5) = 32. a) Find the standard deviation o. b) Find the probability that the number of heads appearing is within 1 standard deviation of the mean. That is, if random variable X= the number of times that heads appears, find P(u -GsXsu+o). a) o = b) To find the probability P(u -osXsu+o) calculate P(X = x) for all integer x in the interval (Simplify your answer. Type your answer in interval notation.) and n them. P(u-osXsu+o) = O (Round to three decimal places as needed.) multiply add
For n successive Bernoulli trials with probability p of success on each trial, the mean number of successes u is given by u= np, and the standard deviation for the number of successes is given by o = /np(1-p). Use this formula to solve the following problem. A fair coin is tossed 64 times. We know that the mean number of times heads appears is p=np = (64)(0.5) = 32. a) Find the standard deviation o. b) Find the probability that the number of heads appearing is within 1 standard deviation of the mean. That is, if random variable X= the number of times that heads appears, find P(u -GsXsu+o). a) o = b) To find the probability P(u -osXsu+o) calculate P(X = x) for all integer x in the interval (Simplify your answer. Type your answer in interval notation.) and n them. P(u-osXsu+o) = O (Round to three decimal places as needed.) multiply add
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For n successive Bernoulli trials with probability p of success on each trial, the mean number of successes u is given by p= np, and the standard deviation for the number of successes is given by o = /np(1-p). Use this formula
to solve the following problem.
A fair coin is tossed 64 times. We know that the mean number of times heads appears is p= np = (64)(0.5) = 32.
a) Find the standard deviation o
b) Find the probability that the number of heads appearing is within 1 standard deviation of the mean. That is, if random variable X= the number of times that heads appears, find P(u -GsXsu+o).
a) o =
b) To find the probability P(u -osXsu+o) calculate P(X= x) for all integer x in the interval
(Simplify your answer. Type your answer in interval notation.)
and
n them.
P(u-asXsu+6) =D
(Round to three decimal places as needed.)
multiply
add
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