Let x be a hypergeometric random variable with N = 15, n = 3, and M = 5.

(a)

Calculate p(0), p(1), p(2), and p(3). (Round your answers to two decimal places.)

p(0)

p(1)

p(2)

p(3)

2) Use the formulas below to calculate ? = E(x) and ?2. (Round your answer for ? to one decimal place and your answer for ?2 to five decimal places.)

? = n(M/N)

?2 = n(M/N)(N ? M/N)(N ? n/N ? 1)

?=

?2=

(d)

What proportion of the population of measurements fall into the interval (? 2?)? (Round your answer to two decimal places.)

What proportion of the population of measurements fall into the interval (? 3?)? (Round your answer to two decimal places.)

Do these results agree with those given by Tchebysheff's Theorem?

yes

no

\fIndicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. 1 = 39 and p = 0.45 O The central limit theorem can be applied. O The central limit theorem cannot be applied.Stat 50, Fall 2020 Pasadena City College Section 6.4: The Central Limit Theorem 11: What is the Central Limit Theorem? What are the requirements (two cases) for Central Limit Theorem? . Case 2:M4A1 Discussion Forum: Central Limit Theorem Discussion Board Topics: 1. Explain the central limit theorem. 2. Why is the central limit theorem an important concept in statistics? Discussion Board Guidelines: You will need to respond to a peer's posting, and evidence of critical thinking is required