Question

suppose that the age of pandas is normally distributed with mean of 25 years and a stdev of 4 years ,

find the probability a random panda lives over 30 years

find the probablity if 4 are randamly selected that they all lived less than 24 hours

what age would panda need to live in order to be among the 10 of the longest living panda

suppose 9 random panda are brought to zoo , what is the probablity that their avg life span will be under 23 years

Answer 1

Solution:

We are given

µ = 25

σ = 4

Find the probability a random panda lives over 30 years

We have to find P(X>30)

P(X>30) = 1 - P(X<30)

Z = (X - µ)/σ

Z = (30 - 25)/4

Z = 1.25

P(Z<1.25) = P(X<30) = 0.89435

(We can find this probability by using either z-table, excel, or any other statistical software)

P(X>30) = 1 - P(X<30)

P(X>30) = 1 - 0.89435

P(X>30) = 0.10565

Required probability = 0.10565

find the probablity if 4 are randamly selected that they all lived less than 24 hours

Solution:

We have to find P(X̄ < 24)

Z = (X̄ - µ)/[σ/sqrt(n)]

Z = (24 - 25)/(4/sqrt(4))

Z = -0.5

P(Z<-0.5) = P(X̄ < 24) = 0.308538

(We can find this probability by using either z-table, excel, or any other statistical software)

Required probability = 0.308538

What age would panda need to live in order to be among the 10 of the longest living panda

We are given

µ = 25

σ = 4

We have to find

X = µ + Z*σ

Z for 10% longest living Pandas = 1.281552

X = 25 + 1.281552*4

X = 30.12621

Required age = 30.13 years

suppose 9 random panda are brought to zoo , what is the probablity that their avg life span will be under 23 years

Solution:

We have to find P(X̄ < 23)

Z = (X̄ - µ)/[σ/sqrt(n)]

Z = (23 - 25)/(4/sqrt(9))

Z = -1.5

P(Z<-1.5) = P(X̄ < 23) = 0.066807

(We can find this probability by using either z-table, excel, or any other statistical software)

Required probability = 0.066807