Many sharks enter a state of tonic immobility when inverted. Suppose that in a p
ID: 3127462 • Letter: M
Question
Many sharks enter a state of tonic immobility when inverted. Suppose that in a particular species of sharks the time a shark remains in a state of tonic immobility when inverted is normally distributed with mean 11.2 minutes and standard deviation 1.1 minutes.
If a biologist induces a state of tonic immobility in such a shark in order to study it, find the probability that the shark will remain in this state for between 10 and 13 minutes.
When a biologist wishes to estimate the mean time that such sharks stay immobile by inducing tonic immobility in each of a sample of 12 sharks, find the probability that mean time of immobility in the sample will be between 10 and 13 minutes.
Explanation / Answer
mean = 11.2
SD = 1.1
P(10<X<13) = P((10-11.2)/1.1<(X-11.2)/1/1<(13-11.2)/1.1)
= P(-1.09<Z<1.63)
= P(1.63) - P(-1.09)
= 0.94845 - 0.13786
= 0.81059
2. P(10<X<13) = P((10-11.2)/(1.1/12^0.5)<(X-11.2)/(1.1/12^0.5)<(13-11.2)/(1.1/12^0.5))
= P(-3.78<Z<5.67)
= P(5.67) - P(-3.78)
= 0.99999 - 0.00008
= 0.99991
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