Question

Consider a normal distribution with mean=88 and standard deviation=80.

Calculate

?P(x overbarxgreater than>25)

for each of the sample sizes below.a.

n=9

b. n=16

a. What is ?P(x overbarxgreater than>25?) when n=9??

?P(x >25?)=

?(Round to four decimal places as? needed.)

Answer 1

Solution :

Given that ,

mean = = 88

standard deviation = = 80

(a)

n = 9

= 88and

= / n = 80 / 9 = 80 / 3

P(? > 25) = 1 - P( < 25) = 1 - P(( - ) / < (25 - 88) / 80/3) = 1 - P(z < -2.3625)

    Using standard normal table,

P( > 25) = 1 - 0.0091 = 0.9909

Probability = 0.9909

(b)

n = 16

= 88 and

= / n = 80 / 16 = 80 / 4 = 20

P(? > 25) = 1 - P( < 25) = 1 - P(( - ) / < (25 - 88) / 20) = 1 - P(z < -3.15)

    Using standard normal table,

P( > 25) = 1 - 0.0008 = 0.9992

Probability = 0.9992