Question

A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why?

Answer 1

If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.

Given sample size is 40, sample mean is 20, sample standard deviation is 5.

We have to find whether the distribution is normally distributed or not.

Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.

Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.

Signs of normal distribution are:

• Symmetric bell shape
• mean and median are equal both located at the center of the distribution
• 68% approximately equals 68% falls within 1 standard deviation of the mean.

Hence the sampling distribution is normally distributed.

Learn more about normal distribution at brainly.com/question/4079902

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