Giant weta, native to New Zealand, are among the largest insects in the world. Their body lengths have a mean of 90 mm and a standard deviation of 3.6 mm.The lengths of a random sample of 36 giant weta is measured. Which of the following is the most accurate description of the distribution of the sample mean length?Select one:a.It is normal with a mean of 90mm and a standard error of 3.6mm.b.It has a mean of 90mm and a standard error of 0.6mm.c.It has a mean of 90mm and a standard error of 3.6mm.d.It is normal with a mean of 90mm and a standard error of 0.6mm.
Question
Giant weta, native to New Zealand, are among the largest insects in the world. Their body lengths have a mean of 90 mm and a standard deviation of 3.6 mm.The lengths of a random sample of 36 giant weta is measured. Which of the following is the most accurate description of the distribution of the sample mean length?Select one:a.It is normal with a mean of 90mm and a standard error of 3.6mm.b.It has a mean of 90mm and a standard error of 0.6mm.c.It has a mean of 90mm and a standard error of 3.6mm.d.It is normal with a mean of 90mm and a standard error of 0.6mm.
Solution
The standard error of the sample mean is calculated using the formula:
SE = σ / √n
where: SE = standard error σ = standard deviation n = sample size
In this case, the standard deviation (σ) is 3.6 mm and the sample size (n) is 36.
Substituting these values into the formula gives:
SE = 3.6 / √36
Calculating the square root of 36 gives 6.
So, SE = 3.6 / 6
This gives a standard error of 0.6 mm.
The distribution of the sample mean length is normal because the sample size is large enough (n > 30).
Therefore, the most accurate description of the distribution of the sample mean length is:
d. It is normal with a mean of 90mm and a standard error of 0.6mm.
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