The Sampling Distribution of a Sample Mean

Sampling Distribution of Difference Between Means

Questions

Question 1 out of 4.
Population $1$ has a mean of $20$ and a variance of $100$ . Population $2$ has a mean of $15$ and a variance of $64$ . You sample $20$ scores from Pop $1$ and $16$ scores from Pop $2$ . What is the mean of the sampling distribution of the difference between means (Pop $1$ - Pop $2$ )?

Question 2 out of 4.
Population $1$ has a mean of $20$ and a variance of $100$ . Population $2$ has a mean of $15$ and a variance of $64$ . You sample $20$ scores from Pop $1$ and $16$ scores from Pop $2$ . What is the variance of the sampling distribution of the difference between means (Pop $1$ - Pop $2$ )?

Question 3 out of 4.
The mean height of

$15$ -year-old boys is

$175$ cm and the variance is

$64$ . For girls, the mean is

$165$ and the variance is

$64$ . If

$8$ boys and

$8$ girls were sampled, what is the probability that the mean height of the sample of boys would be at least

$6$ cm higher than the mean height of the sample of girls?

Question 4 out of 4.
The mean time to complete a task is $727$ millisecond for 3rd graders and $532$ milliseconds for 5th graders. The variances of the two grades are $12,000$ for 3rd graders and $10,000$ for 5th graders. The times for both grades are normally distributed. You randomly sample $12$ 3rd graders and $14$ 5th graders. What is the probability that the mean time of the 3rd graders will exceed the mean time of the 5th graders by $150$ msec or more?