The walking gait of an adult male giraffe is normally distributed

The walking gait of an adult male giraffe is normally distributed with a mean of 8 feet and a standard deviation of 1.2 feet.  Complete the following.

 

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A. Describe the shape and horizontal scaling on the graph of the distribution for the population of all adult male walking gaits (hereafter referred to simply as gaits).

 

B. Find the probability that the gait of a randomly selected adult male giraffe will be less than 7 feet—that is, find P(x < 7).  Based upon your result, state whether or not it is unusual to randomly select an adult male giraffe whose gait is less than 7 (and explain why you chose “unusual” or “not unusual” as your answer).

 

C.  Suppose all possible samples of size 36, taken from the population of all adult male giraffe gaits, are drawn and the mean is found for each resulting sample.  Describe the shape and scaling on the graph of the resulting sampling distribution for the sample mean values.  Hint: Apply the Central Limit Theorem!

 

D. Find the probability that the mean gait of a randomly selected sample of 36 adult male giraffes will be less than 7.2 feet—that is, find P(x-bar < 7.2).  Based upon your result, state whether or not it is unusual to randomly select a sample of 36 adult male giraffes whose mean gait is less than 7.2 (and explain why you chose “unusual” or “not unusual” as your answer).

 

E.  Find the probability that the mean from a sample of 36 gaits will be between 8.0 and 8.25.

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