A random sample of n = 100 observations is selected from a population with mu =

Question

A random sample of n = 100 observations is selected from a population with mu = 30 and sigma = 25. Approximate the probabilities shown below. P(x greaterthanorequalto 28) P(22.1 lessthanorequalto x lessthanorequalto 26.8) P(x lessthanorequalto 28.2) P(x greaterthanorequalto 27.0) P(x greaterthanorequalto 28) = (Round to three decimal places as needed.) P(22.1 lessthanorequalto x lessthanorequalto 26.8) = (Round to three decimal places as needed.) P(x lessthanorequalto 28.2) = (Round to three decimal places as needed.) P(x greaterthanorequalto 27.0) = (Round to three decimal places as needed.)

Explanation / Answer

Mean ( u ) =30
Standard Deviation ( sd )=25
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X > 28) = (28-30)/25
= -2/25 = -0.08
= P ( Z >-0.08) From Standard Normal Table
= 0.5319                  
b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 22.1) = (22.1-30)/25
= -7.9/25 = -0.316
= P ( Z <-0.316) From Standard Normal Table
= 0.376
P(X < 26.8) = (26.8-30)/25
= -3.2/25 = -0.128
= P ( Z <-0.128) From Standard Normal Table
= 0.44907
P(22.1 < X < 26.8) = 0.44907-0.376 = 0.0731                  
c.
P(X > 28.2) = (28.2-30)/25
= -1.8/25 = -0.072
= P ( Z >-0.072) From Standard Normal Table
= 0.5287                  
P(X < = 28.2) = (1 - P(X > 28.2)
= 1 - 0.5287 = 0.4713                  
d.
P(X < 27) = (27-30)/25
= -3/25= -0.12
= P ( Z <-0.12) From Standard Normal Table
= 0.4522                  
P(X > = 27) = (1 - P(X < 27)
= 1 - 0.4522 = 0.5478                  

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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