a normal shaped distribution has mu 200 and standard deviation 30. what are the

Question

a normal shaped distribution has mu 200 and standard deviation 30. what are the zscore values that form the boundaries for the middle 95% of the distributio 1780interactve%20Homework/que2 homework.html?out 6758446 Search 11. A normal shaped distribution has -200 and -30. What are the z-score values that form the boundaries for the middle 95% of the distribution? Please separate your answers with a comma, such as -1,1. Check Answer Not exactly. If.95 is in the middle, what proportion is in each tail? 95% What aze the two z-sooes? beginning Tend problems Iprevious page I next page prt sc

Explanation / Answer

Here, X ~N(µ=200,2=302)

We have to find here value x of X such that P(X<|x|)=0.95.

Consider,

P(X<|x|)=0.95

P(-x<X<x)=0.95

P(X<-x or X>x)=1-0.95=0.05

Due to equal tails ,

P(X>x)=0.05/2=0.025

P((X-µ)/>(x-200)/30)=0.025

P((X-µ)/<(x-200)/30)=0.975

P(Z<(x-200)/30)=0.975 ,where Z=(X-µ)/ ~N(0,1)

which implies (x-200)/30=1.959964 which is Z-score .

Hence the z-score values that form the boundaries for the middle 95% of the distribution are

-1.959964 ,1.959964

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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