a random sample of 36 swimmers have a mean time of 3.91 minutes and a population standard deviation of 0.16 minutes. construct a
2 answers:
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Answer:
Let X the random variable who represents the file sizeof music. We know the following info:
We select a sample of n=50 nails. That represent the sample size.
Since the sample size is large enough n >30, we can use the central limit theorem. From this theorem we know that the distribution for the sample mean is given by:
And we can approximate the distribution of the sample mean as a normal distribution and no matter if the distribution for X is right skewed or no.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Let X the random variable who represents the file sizeof music. We know the following info:
We select a sample of n=50 nails. That represent the sample size.
Since the sample size is large enough n >30, we can use the central limit theorem. From this theorem we know that the distribution for the sample mean is given by:
And we can approximate the distribution of the sample mean as a normal distribution and no matter if the distribution for X is right skewed or no.