Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 5 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the mean is smaller for the x distribution.The probability in part (b) is much higher because the standard deviation is larger for the x distribution.     The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.The probability in part (b) is much higher because the mean is larger for the x distribution.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 4 inches. (a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall? (Round your answer to four decimal places.) (b) If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.) (c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? The probability in part (b) is much higher because the mean is smaller for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution. The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. The probability in part (b) is much higher because the mean is larger for the x distribution. The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of twelve 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution

The probability in part (b) is much higher because the mean is smaller for the x distribution.

1. In a recent survey about US policy in Iraq, 62 % of the respondents said that they support US policy in Iraq. Females comprised 53% of the sample, and of the females, 46% supported US policy in Iraq. A person is selected at random.

1. What is the probability that the person we select is female and supports U.S. policy in Iraq?
2. Are the events "does not support U.S, policy in Iraq" and "female" statistically independent? Why or why not?
3. What is the probability that the person we select is male?
4. What is the probability that the person we select does not support US policy in Iraq?
5. What is the probability that the person we select is female and does not support US policy in Iraq?
6. What is the probability that the person we select is male and does support US policy in Iraq?
7. What is the probability that the person we select is male and does not support US policy in Iraq?
8. Suppose we select a supporter of US policy in Iraq, what is the probability that the person we select is female?
1. ) Suppose we select a person who does not support US policy in Iraq, what is the probability that the person is male?

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 67 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between 66 and 68 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 66 and 68 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the mean is smaller for the x distribution.The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.    The probability in part (b) is much higher because the mean is larger for the x distribution.The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

R Questions Question 2

In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings:

a) The probability of getting six 6's ```{r} #INSERT YOUR ANSWER HERE ```

b) The probability of getting six, seven, or eight 3's ```{r} #INSERT YOUR ANSWER HERE ```

c) The probability of getting six even numbers ```{r} #INSERT YOUR ANSWER HERE ``` ****** ##

Question 3 In a shipment of 20 engines, history shows that the probability of any one engine proving unsatisfactory is 0.1

a) Use the Binomial approximation to calculate the probability that at least three engines are defective? ```{r} #INSERT YOUR ANSWER HERE ```

b) Use the Poisson approximation to calculate the probability that at least three engines are defective? ```{r} #INSERT YOUR ANSWER HERE ```

c) Compare the results of parts a and b, then illustrate on how well the Poisson probability distribution approximates the Binomial probability distribution. ```{r} #INSERT YOUR ANSWER HERE ``` ******

if R code can't be provided that is fine, but will need the answer in simple form if possible with explanation

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of thirty 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.    

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of twelve 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution

The probability in part (b) is much higher because the mean is smaller for the x distribution.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of eighteen 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)

(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 70 inches and standard deviation 1 inches.

(a) What is the probability that an 18-year-old man selected at random is between 69 and 71 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 69 and 71 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

-The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

-The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

-The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

-The probability in part (b) is much higher because the mean is smaller for the x distribution.

-The probability in part (b) is much higher because the mean is larger for the x distribution.