For each of the three writing prompts below, respond with about 110 - 170 words (about one paragraph each).Prompt 1: Suppose the average weekly study time for students at a college is 12.3 hours, wit

For each of the three writing prompts below, respond with about 110 - 170 words (about one paragraph each).

Prompt 1: 

Suppose the average weekly study time for students at a college is 12.3 hours, with a standard deviation of 1.5 hours. Find:

a) The probability that a student chosen at random will have a study time of less than 12 hours.

b) The probability that the average study time of 20  randomly selected students is less than 12 hours.

Explain why the two probabilities are different.

Prompt 2:

Suppose you read a report that states, “65% of all homeowners are planning to make home improvements this year (margin of error is +/- 3%).” Answer these questions:

a) What is the confidence interval and how did you find it?

b) Suppose the confidence interval was found by using a 95% level of confidence. Would the margin of error increase or decrease if the level of confidence was increased. Why?

c) When conducting a survey, how can the study organizers decrease their margin of error without changing the standard 95% level of confidence? Hint: Look at the formula and see which values you can change to make the margin of error smaller. 

Prompt 3: 

Have you ever read about something being “statistically significant?” Write a paragraph about what you think it means, for example, to say something like, “there is a statistically significant difference between the number of bed pillows men have versus the number of pillows women have.”