Question

The length of 1 year old cod from the Scotian Shelf has a
distribution that is approximately normal with a mean of 16 cm
and a standard deviation of 6 cm.

6)The upper and lower deciles are the points that mark out the highest 10% and lowest 10% of the population. Find the upper and lower deciles for the cod length distribution (in cm).

**** Please specify how 1.28 is calculated!!!

Answer 1

Solution :

mean = = 16

standard deviation = = 6

Using standard normal table,

P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 6 + 16 = 23.68

Upper deciles = 23.68 cm

P(Z < z) = 0.10

P(Z < -1.28) = 0.10

z = -1.28

Using z-score formula,

x = z * +

x = -1.28 * 6 + 16 = 8.32

Lower deciles = 8.32 cm