Question

2) A biologist found that Leatherback Sea Turtles have a mean weight of 925 pounds with standard deviation 56 pounds .

a) Find the probability that the weight of a Leatherback would be over 1000 pounds. Round your answer to 3 decimal places.

b) Find the probability that the mean weight of 7 Leatherback would be over 962 pounds. Round your answer to 3 decimal places.

c) Find the probability that the weight of a Leatherback would be between 800 pounds and 880 pounds. Round your answer to 3 decimal places.

d) How heavy would a Leatherback need to be in order to be in the top 7%?

Answer 1

Assuming this to be normally distributed, the distribution here is given as:

a) The probability here is computed as:

P( X > 1000)

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.090 is the required probability here.

b) The sample mean for 7 of them over 962 pounds probability is computed here as:

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.040 is the required probability here.

c) The required probability here is computed as:

P(800 < X < 880)

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.198 is the required probability here.

d) From standard normal tables, we have:

P(Z > 1.476) = 0.07

Therefore the weight required here is:

Therefore 1007.656 pounds is the required weight here.