1 Some variables of interest has a a left skewed distribution with...

1 Some variables of interest has a a left skewed distribution with a mean of 100 and a standard deviation of 10. we take a random sample of size 5.

can we calculate the probability that the sample mean is between 95 and 120? (you do not need to actually calculate the probability for this question.)

a. yes, and the calculated probability would be exact

b. yes, and the calculated probability would be approxiamate

c. no.

2 Some variables of interest has a normal distribution with a mean of 100 and a standard deviation of 10. We take a random sample of size 5.

can we calculate the probability that the sample mean is between 95 and 120? (you do not need to actually calculate the probability for this question.)

a. yes, and the calculated probability would be exact

b. yes, and the calculated probability would be approxiamate

c. no.

3 Some variables of interest has a normal distribution with a mean of 100 and a standard deviation of 10. We take a random sample of size 50.

can we calculate the probability that the sample mean is between 95 and 120? (you do not need to actually calculate the probability for this question.)

a. yes, and the calculated probability would be exact

b. yes, and the calculated probability would be approxiamate

c. no.

4 Some variables of interest has a a left skewed distribution with a mean of 100 and a standard deviation of 10. we take a random sample of size 50.

can we calculate the probability that the sample mean is between 95 and 120? (you do not need to actually calculate the probability for this question.)

a. yes, and the calculated probability would be exact

b. yes, and the calculated probability would be approxiamate

c. no.

5 and 6 heights of professional hockey players follow distribution with mean 186 cm and standard deviation 7 cm.

5 What is the probability that the average height of a random sample of 7 players is greater than 189cm?

keep 4 decimal places in intermediate calculations and report your final answer to 4 decimal places.

6 What is the probability that the average height of a random sample of 12 players is less than 182cm?

keep 4 decimal places in intermediate calculations and report your final answer to 4 decimal places.

7 the weights of organic fertilizer is normally distributed with a mean of 60 pounds and a standard deviation of 2.5 pounds. if we take a random sample of 9 bags of organic fertilizer, there is a 70 % chance that their mean and weight will be less than what value?

keep 4 decimal places in intermediate calculations and report your final answer to 2 decimal places.

8 weights of suitcases checked in at the airport follow a normal distribution with mean 28 pounds and standard deviation 5 pounds. What is the probability that the total weight of a random sample of six suitcases is greater than 180 pounds?

keep 4 decimal places in intermediate calculations and report your final answer to 4 decimal places.

9 Weights of gumballs follow a normal distribution with the mean 10 grams and standard deviation 0.9 grams. We take a random sample of nine gumaballs. According to the 68-95-99.7% rule, there is an approximate 95% chance that the mean weight of the nine gumballs will be between:

a 7.3 grams and 12.7 grams

b 9.7 grams and 10.3 grams

c 8.2 grams and 11.8 grams

d 9.1 grams and 10.9 grams

e 9.4 grams and 10.6 grams