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Chapter 4: Problem 3

Let \(Y\) be \(b\left(72, \frac{1}{3}\right)\). Approximate \(P(22 \leq Y \leq 28)\).

Short Answer

Expert verified
The value can be computed using binomial probability formula over the specified range. As this involves complex calculations, you are recommended to use a statistical software or calculator that has functionality for calculating binomial probabilities.

Step by step solution

01

Understanding the binomial probability

The formula for binomial probability is \( P(x) = C(n, x) * p^x * (1 - p)^{n-x} \) where \( x \) is the number of successes we are calculating the probability for, \( n \) is the number of trials, and \( p \) is the probability of success in a single trial.
02

Calculate \( P(Y) \) for each value of \( Y \)

Using the above formula, find the probability for each value of \( Y \) from 22 to 28 and then sum them to get the total probability.
03

Summing the probabilities

After calculating the probabilities for each value of \( Y \), sum them together to obtain the total probability. This is estimated by \( P(22 \leq Y \leq 28) \).

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