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)

Answer :

Given:
μ = 5.3 cm, population mean
σ = 1.8 cm, population sandard deviation
n = 5, sample size

The random variable is x = .5 cm.
The z-score is
[tex]z = \frac{x-\mu}{\sigma / \sqrt{n} } = \frac{5.5-5.3}{1.8/ \sqrt{5} } =0.2485[/tex]

From standard table, obtain
P(x>5.5) = 1  - 0.598 = 0.402

Answer: 0.402

Answer:

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) = [tex]P(Z>\frac{5.5-5.3}{1.8/\sqrt{5} } =0.2485[/tex]

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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