Answer:
Yes
Explanation:
The z score is a score used in statistics to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}\\\\where\ \mu=mean.\sigma=standard\ deviation, x=raw\ score.\\\\For\ a \ sample\ size\ n:\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For a normal distribution with a mean of μ and standard deviation σ, For any sample size (n) drawn from this population, the sample mean is normally distributed, with mean [tex]\mu_x=\mu[/tex] and standard deviation [tex]\sigma_x=\frac{\sigma}{\sqrt{n } } \\\\[/tex].
Hence given that a mean of μ = 20.6 years and standard deviation σ = 5.3 years, for a sample size of 100:
mean [tex]\mu_x=\mu=20.6\ years[/tex] and standard deviation [tex]\sigma_x=\frac{\sigma}{\sqrt{n } } =\frac{5.3}{\sqrt{100} }=0.53\ years \\\\[/tex].
Based on the computation, it can be deduced that Remy's claim is correct.
It should be noted that the z score is a score that is used to determine by how many standard deviations the raw score is either above or below the mean.
Therefore, based on the information given in the question, the mean of the sampling distribution of the sample mean will be calculated as:
= Standard deviation / Sample size.
= 5.3 / ✓100
= 5.3 / 10 = 0.53
Since the mean of the sampling distribution of the sample means for samples of size 100 is 20.6 years as stated, then the information given is correct.
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