5. Answer the following questions regarding thenormal, standard normal and binom

Question

5. Answer the following questions regarding thenormal, standard normal and binomialdistributions.

(A) What conditions must bemet in order to use the normal distribution to approximate thebinomial distribution?

(B) How does the standardnormal distribution differ from the normaldistribution?

(C) What are the advantages ofusing the standard normal distribution over the normaldistribution?
6. Two yellow marbles areselected, one at a time from a jar of marbles containing 10 black,10 brown, 10 white and 10 green marbles. Let x represent the numberof yellow marbles selected in 2 separate selections from thejar.

(A) If this experiment iscompleted without replacing the marbles each time, explain why x isnot a binomial random variable.

(B) If this experiment iscompleted with replacement of the marbles each time, explain why xis a binomial random variable.
5. Answer the following questions regarding thenormal, standard normal and binomialdistributions.

(A) What conditions must bemet in order to use the normal distribution to approximate thebinomial distribution?

(B) How does the standardnormal distribution differ from the normaldistribution?

(C) What are the advantages ofusing the standard normal distribution over the normaldistribution?
6. Two yellow marbles areselected, one at a time from a jar of marbles containing 10 black,10 brown, 10 white and 10 green marbles. Let x represent the numberof yellow marbles selected in 2 separate selections from thejar.

(A) If this experiment iscompleted without replacing the marbles each time, explain why x isnot a binomial random variable.

(B) If this experiment iscompleted with replacement of the marbles each time, explain why xis a binomial random variable.

Explanation / Answer

5A. The normal distribution is a good approximation to thebinomial when n is sufficiently large, usually n > 30 by thecentral limit theorem. And p is not too close to 0 or 1. Howlarge n needs to be depends on the value of p. If p is near 0.5,the approximation can be good for n much less than20. When np > 5 and n(1 - p) > 5 then it is betterto use caution when using the normal to approximate thebinomial. 5B. Standard normal distribution is centered aroundpoint x = 0, and the area of the curve is equal to1. Generally we consider the normal distribution with arbitrarycenter , and variance 2. 5C. The advantages of the standard normal are that itmakes the computation with its statistics much easier than thenormal distribution. 6A. In order to be a binomial random variable, theprobability for success in each trial must be the same, if we donot replace the marbles after each attempt, the probability ofsuccess changes. 6B. Because the probability of success is the same foreach trial. I Hope that helped

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

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