Question

the weight of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 Kg measurments are recorded to the nearest tenth of a kilogram.

a)draw a sketch of the distribution of poodle weights

b)what is the chance of a poodle weight over 9.8Kg?

c)what is the chance a poodle weight between 7.1 and 8.9 kilogram

d)75% of poodles weigh more than what weight

Answer 1

Solution :

Given that ,

mean = = 8

standard deviation = =0.9

(B)P(x > ) = 1 - P(x<9.8 )

= 1 - P[(x -) / < (9.8 -8) / 0.9]

= 1 - P(z < 2)

Using z table

= 1 - 0.9772

= 0.0228

probability=0.0228

(c)

P(7.1< x <8.9 ) = P[(7.1 -8) /0.9 < (x - ) / < (8.9 -8) / 0.9)]

= P( -1< Z <1 )

= P(Z <1 ) - P(Z < -1)

Using z table   

= 0.8413 -0.1587

   probability= 0.6826

(d)

Using standard normal table,

P(Z > z) = 75%

= 1 - P(Z < z) = 0.75

= P(Z < z ) = 1 - 0.75

= P(Z < z ) = 0.25

= P(Z < -0.67 ) = 0.25

z = -0.67 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= -0.67*0.9+8

x= 7.397

x=7