2. Suppose a random variable W follows a binomial distribution with parameters n = 34 and p 0.73; that is, W~Bin(34,0.73). Rounding to 4 decimal places where necessary: a. Calculate P(W = 26). - b. Calculate P(W > 31). c. Calculate P(24 < W ≤ 30). d. What is the probability that W is within one standard deviation of E(W), the expected value of W?

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### Binomial Distribution Problem

**Problem 2:**
Suppose a random variable \( W \) follows a binomial distribution with parameters \( n = 34 \) and \( p = 0.73 \); that is, \( W \sim \text{Bin}(34, 0.73) \). Rounding to 4 decimal places where necessary:

a. Calculate \( P(W = 26) \).

b. Calculate \( P(W > 31) \).

c. Calculate \( P(24 < W \leq 30) \).

d. What is the probability that \( W \) is within one standard deviation of \( E(W) \), the expected value of \( W \)?
Transcribed Image Text:### Binomial Distribution Problem **Problem 2:** Suppose a random variable \( W \) follows a binomial distribution with parameters \( n = 34 \) and \( p = 0.73 \); that is, \( W \sim \text{Bin}(34, 0.73) \). Rounding to 4 decimal places where necessary: a. Calculate \( P(W = 26) \). b. Calculate \( P(W > 31) \). c. Calculate \( P(24 < W \leq 30) \). d. What is the probability that \( W \) is within one standard deviation of \( E(W) \), the expected value of \( W \)?
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