Question

The northern arborial cat gives birst to 1 - 3 kittens after a gestational length that is a continuous random variable that has a normal distribution with a mean of 42 days and standard deviation of 8 days. Round the following to the nearest 10th of a day.

How many days mark the first quartile of northern arborial cat gestational lengths?

How many days mark the 70 th percentile of northern arborial cat gestational lengths?

How many days long is northern arborial cat gestation so that only 15 % of pregnancies are longer?

Answer 1

Solution:-

Given that,

mean = = 42

standard deviation = = 8

Using standard normal table,

The z dist'n 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,

x = z * +

x = -0.6745 * 8 + 42

x = 36.60

x = 37

Answer :- 37 days

Using standard normal table,

P(Z < z) = 70%

= P(Z < z ) = 0.70

= P(Z < 0.524 ) = 0.70

z = 0.524

Using z-score formula,

x = z * +

x = 0.524 * 8 + 42

x = 46.19

x = 46

Answer :- 46 days

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z ) = 0.15

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.036 ) = 0.85  

z = 1.036

Using z-score formula,

x = z * +

x = 1.036 * 8 + 42

x = 50.29

x = 50

Answer :- 50