The basal diameter of a sea anemone is an indicator of its age, and in a certain population of anemones, the distribution of basal diameters is approximately normal with a mean of 5.3 cm and a standard deviation of 1.8 cm. suppose you randomly select five anemones from this population. a. what is the probability that all five anemones have a basal diameter more than 5.5 cm? (2pt)

Step-by-step explanation:

Let X be the basal diameter of a sea anemone.

Given that X is N(5.3, 1.8)

Sample size =5

We have to find the prob that all five anemones have a basal diameter more than 5.5 cm

Prob (for one anemone >5.5 cm) =

Since each anemone selected is independent of the other anemone, the selected anemones follow Binomial with n =5 and p = 0.2485 and q=0.7515

P(X=5) = 1-P(X=0) = 1-0.7515^5

=0.7603

Note that 5 elements selected cannot be taken as normal since sample size is small.

No of anemones selected having a basal diameter more than 5.5 cm is

binomial with n=5 and p = 0.2585

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