The walking gait of an adult male giraffe is normally distributed with a mean of
ID: 3134975 • Letter: T
Question
The walking gait of an adult male giraffe is normally distributed with a mean of 10 feet and a standard deviation of 1.5 feet. Complete the following. (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 8.5 feet---that is, find P(x < 8.5). Based upon your result, state whether or not it is unusual to randomly select an adult male giraffe whose gait is less than 8.5 (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! The walking gait of an adult male giraffe is normally distributed with a mean of 10 feet and a standard deviation of 1.5 feet. Complete the following. (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 8.5 feet---that is, find P(x < 8.5). Based upon your result, state whether or not it is unusual to randomly select an adult male giraffe whose gait is less than 8.5 (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!Explanation / Answer
a)
It is bell shaped with standard deviation of 1.5 feet, so we mark in intervals for 1.5 feet in the graph, with respect to the mean.
**********************
b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 8.5
u = mean = 10
s = standard deviation = 1.5
Thus,
z = (x - u) / s = -1
Thus, using a table/technology, the left tailed area of this is
P(z < -1 ) = 0.158655254 [ANSWER]
As it is not less than 0.05, it is NOT UNUSUAL. [ANSWER]
**********************
c)
By central limit theorem, with the same mean as population mean
u(X) = u = 10
and a reduced standard deviation of
sigma(X) = sigma/sqrt(n) = 1.5/sqrt(36) = 0.25 [ANSWER]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.