Activity One: Sampling Distribution and Central Limit Theorem In each situation, nominate whether the sampling distribution...

Activity One: Sampling Distribution and Central Limit Theorem

In each situation, nominate whether the sampling distribution of the sample mean can be assumed to be normally distributed or not?

The population age is normally distributed, with a mean of 45 years and standard deviation of 12 years. These statistics are based on 25 observations.

The population sales are uniformly distributed, with a mean of $600 and standard deviation of $2. These statistics are based on 12 observations.

The population time is uniformly distributed, with a mean of 11 minutes and standard deviation of 3 minutes. These statistics are based on 52 observations.

A proportion mean of 30% is calculated. These are based on 25 observations from the population.

Solutions

Expert Solution

1. The population age is normally distributed, with a mean of 45 years and standard deviation of 12 years. These statistics are based on 25 observations.

Ans: Yes, the sampling distribution of the sample mean can be assumed to be normally distributed for this data.

2. The population sales are uniformly distributed, with a mean of $600 and standard deviation of $2. These statistics are based on 12 observations.

Ans: No, the sampling distribution of the sample mean can not be assumed to be normally distributed for this data because the sample size is too small for assuming a normal distribution.

3. The population time is uniformly distributed, with a mean of 11 minutes and standard deviation of 3 minutes. These statistics are based on 52 observations.

Ans: Yes, the sampling distribution of the sample mean can be assumed to be normally distributed for this data because the sample size is large enough for assuming a normal distribution.

4. A proportion mean of 30% is calculated. These are based on 25 observations from the population.

Ans: No, the sampling distribution of the sample mean can not be assumed to be normally distributed for this data because the sample size is not large enough for assuming a normal distribution that is 0.30*25=7.5 is less than 10.

orchestra answered 1 year ago

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