1 and 2 heights of professional hockey players follow distribution with mean 186 cm and standard deviation 7 cm.

1 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.

2 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.

3 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.

4 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.

5 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

6 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.

7 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.

8 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.

9 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 os 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.

10 suppose the IQ's of adult Canadians follow a normal distribution with standard deviation 15. A random sample os 30 adult Canadians has a mean IQ of 112.

We would like to construct a 97% confidence interval for the true mean IQ of all adult Canadians. What is the critical value z* to be used in the interval? (you do not need to calculate the confidence interval. Simply find z*. input a positive number.

report answer to 2 decimal places

11 It is known that the amount of water adults drink per day follows a normal distribution with standard deviation 200 ml. A random sample of 50 adults is selected and it is found that their mean daily water intake is 1725ml.

What is the margin error for a 95 % confidence interval for the true mean daily water consumption of adults? (you do not need to calculate the entire confidence interval. The margin of error is simply the right side of the sign in a confidence interval.)

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

12 We would like to construct a confidence interval for the mean of some population. Which of the following combinations of confidence level and sample size will produce the narrowest interval?

a 99% confidence, n= 30

b 90% confidence, n=35

c 95% confidence, n=35

d 95% confidence, n=30

c 90% confidence, n=30

13 It is calculated that, in order to estimate the true mean amount of money spent by all customers at a grocery store to within $3 with 90% confidence, we require a sample of 50 customers. What sample size would be required to estimate the true mean to within $1 with 90%?

answer

14 and 15 suppose that 40% of students at a university drive to campus

14 if we randomly select 200 students from this university, what is the approximate probability that less than 35% of them drive to campus?

keep 6 decimal places in intermediate calculations and report your final answer to 4 decimal places.

15 if werandomly select 50 students from this university, what is the approximate probability that more than 25 of them drive to campus?

keep 6 decimal places in intermediate calculations and report your final answer to 4 decimal places.

16 the size of farms (in acres) in a U.S state follow a normal distribution with known standard deviation. We would like to estimate the true mean size of all farms in the state. We measure the sizes of a random sample of 30 farms and calculate a 95% confidence interval for to be (290, 310). What is the correct interpretation of this interval?

a in repeated samples of 30 farms, 95% of similarly constructed intervals will contain the population mean.

b in repeated samples of 30 farms, 95% of similarly constructed intervals will contain the same mean.

c The probability that the population mean is between 290 and 310 acres is 0.95

d approximately 95% of farms have size between 290 and 310 acres

e approximately 95% of sample of 30 farms will have a mean size between 290 and 310 acres.