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 38 days and standard deviation of 4.5 days. Round the following to four decimal places. What is the probability that a pregnant northern arborial cat gives birth after more than 40 days?   What is the probability that a pregnant northern arborial cat gives birth is less than 34 days?   What is the probability that a pregnant northern arborial cat gives birth in between 32 and 42 days?   What is the probability that a pregnant northern arborial cat gives birth in exactly 38 days?   A northern arborial cat pregnancy is considered abnormal if is less than 28 days or more than 44 days. What is the probability that a pregnant northern arborial cat experiences an abnormal pregnancy?

	2.	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 38 days and standard deviation of 4.5 days. Round the following to the nearest day. How many days mark the first quartile of northern arborial cat gestational lengths? How many days mark the 80th percentile of northern arborial cat gestational lengths? How many days long is northern arborial cat gestational length so that only 15% of gestational lengths are longer?

Answer 1

Question 1:

What is the probability that a pregnant northern arborial cat gives birth after more than 40 days?  

z = (x - µ)/σ = (40 - 38)/4.5 = 0.44

P(z > 0.44) = 0.3284

What is the probability that a pregnant northern arborial cat gives birth is less than 34 days?

z = (x - µ)/σ = (34 - 38)/4.5 = -0.89

P(z < -0.89) = 0.1870

What is the probability that a pregnant northern arborial cat gives birth in between 32 and 42 days?  

z = (x - µ)/σ = (32 - 38)/4.5 = -1.33

P(z < -1.33) = 0.0912

z = (x - µ)/σ = (42 - 38)/4.5 = 0.89

P(z < 0.89) = 0.8130

Required probability = 0.8130 - 0.0912 = 0.7218

What is the probability that a pregnant northern arborial cat gives birth in exactly 38 days?

z = (x - µ)/σ = (38 - 38)/4.5 = 0

P(z = 0.5) = 0.5000

A northern arborial cat pregnancy is considered abnormal if is less than 28 days or more than 44 days.

What is the probability that a pregnant northern arborial cat experiences an abnormal pregnancy?  

z = (x - µ)/σ = (28 - 38)/4.5 = -2.22

P(z < -2.22) = 0.0131

z = (x - µ)/σ = (44 - 38)/4.5 = 1.33

P(z > 1.33) = 0.0912

Required probability = 0.0131 + 0.0912 = 0.1043

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