Question

Suppose x has a distribution with ? = 17 and ? = 16. (a) If a random sample of size n = 39 is drawn, find ?x, ? x and P(17 ? x ? 19). (Round ?x to two decimal places and the probability to four decimal places.)

?x =

? x =

P(17 ? x ? 19) =

If a random sample of size n = 62 is drawn, find ?x, ? x and P(17 ? x ? 19). (Round ? x to two decimal places and the probability to four decimal places.)

?x =

? x =

P(17 ? x ? 19) =

Answer 1

Solution:

Given that,

= 17

= 16

a ) n = 39

So,

= 17

=  ( /n) = ( 16 / 39 ) = 2.56

p ( 17     19 )

= p ( 17 - 17 / 2.56 ) ( -  /   ) ( 19 - 17 / 2.56)

= p (0 / 2.56   z   2 /2.56)

= p (0   z     0.78)

= p ( z 0.78) - p ( z   0 )

Using z table

= 0.7823 - 0.5000

= 0.2823

Probability = 0.2823

b )n = 62

So,

= 17

=  ( /n) = ( 16 / 62 ) = 2.03

p ( 17     19 )

= p ( 17 - 17 / 2.03 ) ( -  /   ) ( 19 - 17 / 2.03)

= p (0 / 2.03    z    2 /2.03)

= p (0   z     0.78)

= p ( z 0.99) - p ( z   0 )

Using z table

= 0.8389 - 0.5000

= 0.3389

Probability = 0.3389