the following table gives the monthly salary of 6 employees of a certain supermarket (in thousand of pesos). suppose that random of sample of size 4 are taken from this population of six employees
Answer:
1. Mean: 17
Variance: 20
Standard Deviation: 4.47
2. The histogram would show a normal distribution with a mean of 17 and a standard deviation of 4.47.
3. The mean of the sampling distribution of the sample means is equal to the population mean, and the variance of the sampling distribution of the sample means is equal to the population variance divided by the sample size.
Step-by-step explanation:
1. The mean of the population is calculated by adding all the values and dividing by the number of values. The variance is calculated by subtracting the mean from each value, squaring the result, adding all these squared results, and dividing by the number of values. The standard deviation is the square root of the variance.
2. A histogram of the sampling distribution of the population mean would show a normal distribution with a mean of 17 and a standard deviation of 4.47. This is because the sampling distribution of the mean is normally distributed if the population is normally distributed, and the mean of the sampling distribution is equal to the population mean.
3. The mean of the sampling distribution of the sample means is equal to the population mean, and the variance of the sampling distribution of the sample means is equal to the population variance divided by the sample size. This is a result of the Central Limit Theorem, which states that the sampling distribution of the mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
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