Probabily example, Mathematics

A sample of students had a mean age of 35 years along with a standard deviation of 5 years. A student was randomly picked from a group of 200 students. Determine the probability that the age of the student turned out to be as given below:

i. Lying in between 35 and 40

ii. Lying in between 30 and 40

iii. Lying in between 25 and 30

iv. Lying beyond 45 yrs

v. Lying beyond 30 yrs

vi. Lying below 25 years

Solution

(i). The standardized value for 35 years

            Z =  (x - μ)/s   =  (35-35)/5 =  0

The standardized value for 40 years

Z = (x - μ)/s    = (40- 35)/5   =            1

∴  the area between Z = 1 and Z = 0 is 0.3413. These values are checked from the general tables

The value from standard common curve tables

While z = 0, p = 0

And while z = 1, p = 0.3413

Now the area under this curve is the area between z = 0 and z = 1

= 0.3413 - 0 = 0.3413

∴  the probability age lying among  35 and 40 yrs is  0.3413

(ii). 30 and 40 years

Z = (x - μ)/s =  (30 - 35)/5 = -5/5 = -1

Z = (x - μ)/s    = (40 - 35)/5 = 5/5 = 1

 ∴ The area between Z = 1 and Z = -1 is = 0.3413 as lying on the positive side of zero + 0.3413 as lying on the negative side of zero

P = 0.6826

∴  the probability age lying between 30 and 40 yrs is  0.6826

(iii). 25 and 30 years

            Z =  (x - μ)/s   = (25 - 35)/5 = -10/5 = -2

            Z = (x - μ)/s =  (30 - 35)/5 = -5/5 = -1

∴  the area between Z = -2 and Z = -1

Probability area corresponding to Z = -2

            = 0.4772 (the z value to check from the tables is 2)

Probability area corresponding to Z = -1

            = 0.3413 (the z value for this case is 1)

∴  the probability that the age lies between 25 and 30 yrs

            = 0.4772 - 0.3413 the area under this curve

            P = 0.1359

iv). P(beyond 45 years) is verified as given = P(x > 45)

Z  = (x - μ)/s =  (40 - 35)/5 = 10/5 = +2

Probability corresponding to Z = 2  = 0.4772 = probability of between 45 and 35

∴  P(Age > 45yrs) = 0.5000 - 0.4772

= 0.0228

Posted Date: 2/20/2013 6:42:41 AM | Location : United States







Related Discussions:- Probabily example, Assignment Help, Ask Question on Probabily example, Get Answer, Expert's Help, Probabily example Discussions

Write discussion on Probabily example
Your posts are moderated
Related Questions
I need help with my homework, I am to the edge right now with this w=5pq/2

E1) What is the difference between the two models listed above? Which is more difficult for children to understand? E2) List some activities and word problems that you would exp


Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0

John and Charlie have a whole of 80 dollars. John has x dollars. How much money does Charlie have? This problem translates to the expression 42 + (11 - 9) ÷ 2. Using order of o

The point which divides a gven line - segment externally: Construction : i )Draw BX making an actue angle at B. ii) Starting from B mark three equal points on BX as sh

Divide 6.8 × 10 5 by 2.0 × 10 2 . Write your answer in scientific notation? To divide numbers written in scienti?c notation and divide the ?rst numbers (6.8 ÷ 2.0 = 3.4); the

Can you help me with what goes into 54

how to get the objective report?