Question

A sample of size 27 will be drawn from a population with mean 4 and standard deviation 3.

(a) Is it appropriate to use the normal distribution to find probabilities for x?

(b) If appropriate find the probability that x will be greater than 2.

(c) If appropriate find the

40th percentile of x.

Answer 1

Solution :

Given that,

mean = = 4

standard deviation = =3

n=27

= =4

= / n = 3 / 27=0.5774

P( >2 ) = 1 - P( <2 )

= 1 - P[( - ) / < (2-4) /0.5774 ]

= 1 - P(z <-3.46)

Using z table

= 1 - 0.0003

= 0.9997

probability=0.9997

(B)

Using standard normal table,

P(Z < z) =40 %

= P(Z < z) = 0.40  

= P(Z <-0.25 ) = 0.40

z = -0.25 Using standard normal table,

Using z-score formula  

= z * +

=-0.25 *0.5774 +4

= 3.86