Question

A random sample of n= 100 observations is selected from a population with u = 29 and o = 17. Approximate the probabilities shown below. a. P(x228) b. P(22.1sxs 26.8) c. P(xs 28.2) d. P( x270) Click the icon to view the table of normal curve areas.

Answer 1

Given a random sample of size n=100 is selected from the population with

u= 29,0 = 17

a)

PT> 28) = 1 - Plī<28)

PC&2 28) = 1 – pils

28 – 29 Plī> 28) = 1 - P(Z < 100

P(T > 28) = 1 - P(Z <

PT> 28) = 1 - P(Z <

PT> 28) = 1 - P(Z < -0.588)

PT> 28) = 1 - P(Z < -0.59)

##By using z table

PT> 28) = 1 -0.2810

PT> 28) = 0.719

b)

26.8 s P(22.1 <ī < 26.8) = P - 11

26.8 – 29 22.1 - 29 P(22.1 <i < 26.8) = P( -<2< 1.7 1.7

-6.9 P(22.1 < i < 26.8) = PGD<z« 7,2 1.7 17

P(22.1 <ī < 26.8) = P(-4.06 << -1.29)

P(22.1 <ī < 26.8) = P(-4.06 << -1.29)

P(22.1 <ī < 26.8) = P(Z < -1.29) - P(Z < -4.06)

### By using z table

P(22.1 < i < 26.8) = 0.0985 – 0.00003167

P(22.1 < i < 26.8) = 0.09846833

c)

28.2- Pī < 28.2) = P(Z <

28.2 – 29 Pī < 28.2) = P(Z < 1.7

-0.8 Pī < 28.2) = P(Z <

Plī< 28.2) = P(Z < -0.47)

## By using z table.

Plī< 28.2) = 0.3192

d)

PT> 27) = 1 - Plī<27)

PT> 27) = 1- P(Z <27 – 29 17

PT> 27) = 1- P(Z <

PT> 27) = 1 - P(Z < -1.18)

## By using z table.

PT> 27) = 1 -0.1190

PT> 27) = 0.881