Given a normal population with mean 250 and standard deviation 10 (a) Should P(X

Question

Given a normal population with mean 250 and standard deviation 10 (a) Should P(X 259) be greater or smaller than 0.5? (b) For which sample size, n = 30 or n = 20 would P(X 259) be greater? (Hint: can be explained without computing both probabilities) (c) For which sample size, n = 30 or n = 20 would P(X > 265) be greater? (Hint: can be explained without computing both probabilities) Given a normal population with mean 250 and standard deviation 10 (a) Should P(X 259) be greater or smaller than 0.5? (b) For which sample size, n = 30 or n = 20 would P(X 259) be greater? (Hint: can be explained without computing both probabilities) (c) For which sample size, n = 30 or n = 20 would P(X > 265) be greater? (Hint: can be explained without computing both probabilities) (a) Should P(X 259) be greater or smaller than 0.5? (b) For which sample size, n = 30 or n = 20 would P(X 259) be greater? (Hint: can be explained without computing both probabilities) (c) For which sample size, n = 30 or n = 20 would P(X > 265) be greater? (Hint: can be explained without computing both probabilities)

Explanation / Answer

Ans:

a)

z=(259-250)/10=0.9

P(z<=0.9)=0.8159 i.e. greater than 0.5

b)Larger the sample size,larger the z score,larger the probablity P(X<=259)

hence,for n=30,P(X<=259) will be greater.

c)Larger the sample,larger the z score,smaller the P(X>265)

hence,for n=20, P(X>265) will be greater.

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

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