Question

1. The weight of an 8 month old grizzly cub is given by a normal distribution with m =183.5 lbs. and

s = 17.0 lbs.;                   

1. Find the first quartile.

Find the standardized (z) score for the data point 205.0 lbs.

Answer 1

Solution :

Given that,

mean = M = 183.5

standard deviation = S = 17.0

n = 8

M = 183.5

S_M = S / n =  17.0 8 = 6.0104

a ) Using standard normal table,

The First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.6745

Using z-score formula,

= z * S_M + M

= -0.67 * 6.0104 + 183.5

= 179.47

First quartile =179.5 lbs

b ) = 205.0

Using z-score formula,

Z = - M /S_M

= (205.0 -183.5 ) / 6.0104

= 21.5 / 6.0104

=3.577

Z = 3.58