Question

It is 2075 and Stella, an amateur astronomer, recently was watching rocket launches on a Saturday at the newly completed spaceport in Arizona. She likes to try to guess what type of load the rocket was based on first stage burn time. She knows that for military launches that the burn time is N(101 seconds, 841 seconds^2).

1. What type of data is Stella measuring?

-Categorical, Ordinal

-Numerical, Interval

-Numerical, Ratio

-Categorical, Nominal

2. The first launch of the day had a first stage burn time of 153. What percentage of military launches would have a burn time greater than what Stella saw?

3. The next launch of the day had a first stage burn time of 45. What percentage of military launches would have a burn time between the two launches that Sella saw?

4. Stella knows that on any given day, only one group gets to launch rockets (military, weather, media, etc). She randomly samples a total of 43 rockest to measure today and finds that their mean launch time is 104. How many standard deviations away and direction from the population mean is her sample assuming all of the launches she saw were in fact military?

5. Stella's buddy Cindy just let her know that the distribution of the military rockets actually is not normally distributed, infact it is closer to uniform. Stella realizes that if this is true she may need to rethink her conclusions. Select all of the statements that would be true with the new information:

a.) Part 4: The central limit theorem does not apply as the original distribution is no longer normal so the sample distribution will not be normal.

b.) Part 2 & 3: the population mean will be different, therefore probabilities will be different.

c.) Part 4: No change as my sample size still lets me use the central limit theorem.

d.) Part 2 & 3: the shape of the distribution will be different, therefore probabilities between the points will likely be different.

e.) Part 2 & 3: the population standard deviation will be different, therefore probabilities will be different.

Answer 1

1:

Numerical, Ratio

2:

Here we have

The z-score for X = 153 is

The percentage of military launches would have a burn time greater than what Stella saw is

Answer: 3.67%

3:

The z-score for X = 45 is

The percentage of military launches would have a burn time between the two launches that Sella saw is

4)

The z-score for is

Answer: 0.68 standard deviations above mean

5:

c.) Part 4: No change as my sample size still lets me use the central limit theorem.

d.) Part 2 & 3: the shape of the distribution will be different, therefore probabilities between the points will likely be different.