7. Using tables to calculate probabilities from the normal distribution As Aa Us

Question

7. Using tables to calculate probabilities from the normal distribution As Aa Use the following unit normal tables and accompanying figures to determine the probability that a z-score value would fall within each of the specified ranges. To use the tables, click on the Unit Normal Tables tab beneath the figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the normal distribution corresponding to that range of 2-scores will appear. If you need a different range of z-scores simply click on the box again and select a new range. Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the appropriate probability. 1. p(z > 3.6) 3. p(z

Explanation / Answer

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P(X > 3.6) = (3.6-0)/1
= 3.6/1 = 3.6
= P ( Z >3.6) From Standard Normal Table
= 0.0002

b.
P(X < 3.8) = (3.8-0)/1
= 3.8/1= 3.8
= P ( Z <3.8) From Standard Normal Table
= 0.9999                  

c.              
P(X > -1.9) = (-1.9-0)/1
= -1.9/1 = -1.9
= P ( Z >-1.9) From Standard Normal Table
= 0.9713                  

d.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.9) = (0.9-0)/1
= 0.9/1 = 0.9
= P ( Z <0.9) From Standard Normal Table
= 0.81594
P(X < 1.9) = (1.9-0)/1
= 1.9/1 = 1.9
= P ( Z <1.9) From Standard Normal Table
= 0.97128

e.
P(0.9 < X < 1.9) = 0.97128-0.81594 = 0.1553                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -3.2) = (-3.2-0)/1
= -3.2/1 = -3.2
= P ( Z <-3.2) From Standard Normal Table
= 0.00069
P(X < 1.2) = (1.2-0)/1
= 1.2/1 = 1.2
= P ( Z <1.2) From Standard Normal Table
= 0.88493
P(-3.2 < X < 1.2) = 0.88493-0.00069 = 0.8842

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

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