Question

The length of an adult oceanic manta ray is normally distributed with a mean of 14.9 ft and a standard deviation of 3.65 ft. One adult oceanic manta ray is selected at random, and we are interested in its length.
a) Define the random variable of interest.
b) State the distribution of the RV of interest.
c) What is the probability that its length is between 12 and 16 ft?
d) What is the probability that its length is less than 13 ft or at least 15 ft?
e) What is the length that is at the 96th percentile?

Answer 1

a) Let X be the  variable of interest is the length of an adult oceanic manta ray in ft.

b) Since , the distribution of X is normal distribution with mean 14.9 ft and standard deviation 3.65 ft.

i.e.

c) Now ,

; From the standard normal probability table

Therefore , probability that its length is between 12 and 16 ft is 0.4031

d) Now ,

  ; From the standard normal probability table

e) Now ,

..................(I)

From the standard normal probability table

................(II)

From (I) and (II) , we get,

Therefore , the length of the 96th percentile is 21.2875 ft.