Stat 200 Quiz 2 | Complete Solution

Quiz 2 Stat 200

Instructions: Record your answers and work in the space below each problem. Be sure to record the final answer next to “Answer” and show all your calculation steps or assumptions under “Work.” You can type in your calculations, use the equation tool, or insert images of your handwritten calculations. If you have a tablet with a stylus, it may even be possible to write directly into the table cell. Whatever you do, make sure it is clear and neat. Thanks.
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Problem Number    Problem and Solution
#1
(5 pts)    1. Forty percent of the UMUC faculty teach online classes and 25% of the faculty teach part time. Of the part time faculty, 60% have taught an online class. Let A = event that a UMUC faculty member teaches an online class and B = event that a UMUC faculty member is part time.

a. Find P(A AND B).
b. Find P(B|A).
c. Find P(A OR B).
d. Using an appropriate test, show whether A and B are independent.
e. Using an appropriate test, show whether A and B are mutually exclusive.
    Answer:

Work:
#2
(5 pts)    Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean μ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them.

a. 11 kg
b. 7.9 kg
c. 12.2 kg       

    Answer:

Work:
#3
(5 pts)    In 2015, the average length of Hillary Clinton’s emails were 174 words, with a standard deviation of 55 words. Suppose we randomly pick 38 of her emails from 2015.

a. In words, Χ = _____________
b. In words, X ¯ = _____________
c. X ¯ ~ _____(_____,_____)
d. The IQR for X ¯  =
    Answer:

Work:

#4
(5 pts)    The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.
a. In words, X = _____________
b. In words, X ¯ = ___________________
c. X ¯ ~ _____(_____,_____)
d. In words, ΣX = _______________
e. ΣX ~ _____(_____,_____)
f. Is it likely that an individual stayed more than five days in the hospital? Why or why not?
g. Is it likely that the average stay for the 80 women was more than five days? Why or why not?
h. Which is more likely:
       1.  An individual stayed more than five days.
       2. The average stay of 80 women was more than five days.
i. If we were to sum up the women’s stays, is it likely that, collectively they spent more than a year in the hospital?
    Answer:

Work: