Central Limit Theorem for Sums

An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.

Find the probability that the sum of the 95 values is greater than 7,650.

(give the answer to 4 decimal places)

An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.

Find the probability that the sum of the 95 values is less than 7,400.

(give the answer to 4 decimal places)

An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.

Find the sum that is two standard deviations above the mean of the sums.

(give the answer to 2 decimal places)

An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.

Find the sum that is 1.5 standard deviations below the mean of the sums.

(give the answer to 2 decimal places)

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

Find the probability that the sum of the 40 values is greater than 7,500.

(give the answer to 4 decimal places)

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

Find the probability that the sum of the 40 values is less than 7,000.

(give the answer to 4 decimal places)

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

Find the sum that is one standard deviation above the mean of the sums.

(give the answer to 2 decimal places)

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

Find the sum that is 1.5 standard deviations below the mean of the sums.

(give the answer to 2 decimal places)

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

Find the percentage of sums between 1.5 standard deviations below the mean of the sums and one standard deviation above the mean of the sums.

(give the answer to 2 decimal places)

A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100.

. Find the probability that the sum of the 100 values is greater than 3,910.

(give the answer to 4 decimal places)