Answer:
The point estimate for the population standard deviation of the length of the walking canes is 0.16.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex].
In this problem
The point estimate of the standard deviation is the standard deviation of the sample.
In a sample of 83 walking canes, the average length was found to be 34.9in. with a standard deviation of 1.5. By the Central Limit Theorem, we have that:
[tex]s = \frac{1.5}{\sqrt{83}} = 0.16[/tex]
The point estimate for the population standard deviation of the length of the walking canes is 0.16.
