Please answer everything i just guessed! thank you The amounts of time employees

Question

Please answer everything i just guessed! thank you

The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.5 hours and a standard deviation of 0.35 hour. Random samples of size 23 and 37 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases? If the sample size is n = 23, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is 1. (Type an integer or a decimal.) The standard deviation of the distribution of sample means is 1. (Round to two decimal places as needed.) If the sample size is n = 37, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is 1. (Type an integer or a decimal.) The standard deviation of the distribution of sample means is (Type an integer or decimal rounded to the nearest hundredth as needed.) What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases? Choose the correct answer below. The mean and the standard deviation both increase. The mean stays the same, but the standard deviation decreases. The mean and the standard deviation both decrease. The mean stays the same, but the standard deviation increases.

Explanation / Answer

The central limit theorem states that: Given a population with a finite mean and a finite non-zero variance 2, the sampling distribution of the mean approaches a normal distribution with a mean of and a variance of 2/N as N, the sample size, increases.

So based on this

For n=23, mean=7.5 and sd=0.35/sqrt(23)=0.07

For n=37, mean=7.5 and sd=0.06

So we can see that mean will be same but standard deviation of sampling mean decreases as we increase sample size. So B is correct answer

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