23, 32% of women consider the considers herself a fan of professional baseball.

Question

23, 32% of women consider the considers herself a fan of professional baseball. Complete parts (a) through (d) below. es fans of professional baseball. You randomly select six women and ask each if she (a) Find the mean of the binomial distribution (Round to the nearest tenth as needed.) (b) Find the variance of the binomial distribution. (Round to the nearest tenth as needed.) (c) Find the standard deviation of the binomial distribution = (Round to the nearest tenth as needed.) (d) Interpret the results in the context of the real-life situation. On average, would differ from the mean by no more than out of 6 women would consider themselves baseball fans. The standard deviation is women, so in most samples of 6 women, the number of women who consider themselves baseball fans (Type integers or decimals rounded to the nearest tenth as needed.) 10/

Explanation / Answer

n = 23

P = 0.32

P(X = 6) = 23C6 * (0.32)^6 * (0.68)^17 = 0.15

A) mean = n * P = 6 * 0.15 = 0.9

B) Variance = n * P * (1 - P ) = 6 * 0.15 * 0.85 = 0.8

C) standard deviation = sqrt (0.8) = 0.9

D) P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 23C0 * (0.32)^0 * (0.68)^23 + 23C1 * (0.32)^1 * (0.68)^22

+ 23C2 * (0.32)^2 * (0.68)^22 + 23C3 * (0.32)^3 * (0.68)^20 +

23C4 * (0.32)^4 * (0.68)^19 + 23C5 * (0.32)^5 * (0.68)^18 +23C6 * (0.32)^6 * (0.68)^17 = 0.4

Mean = 6 * 0.4 = 3.4

Standard deviation = sqrt(n * P * (1 - P))

= Sqrt(6 * 0.4 * 0.6 ) = 1.2

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.