Question

A sample of size 24 will be drawn from a population with mean 106 and standard deviation 34

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

(b) If appropriate find the probability that x will be less than 94.

(c) If appropriate find the 95th percentile of x

.

Answer 1

Solution :

Given that ,

mean =   = 106

standard deviation = =34

n = 24

= 106

=  / n = 34/ 24=6.9402

A)yes it is appropriate to use the normal distribution to find probabilities for x

(B)P( <94 ) = P[( - ) / < (94-106) /6.9402 ]

= P(z <-1.73 )

Using z table  

=0.0418   

probability= 0.0418   

(c)

Using standard normal table,

P(Z < z) = 95%

= P(Z < z) = 0.95  

= P(Z < 1.64) = 0.95

z = 1.64 Using standard normal z table,

Using z-score formula  

x= z * +

x= 1.64 *6.9402+106

x= 117.38