Project #64787 - Epidemiology and BioStatistics Probability

Suppose a couple has four children. Assume that each child is equally likely to be a boy or a girl, regardless of the outcome of previous births. The following table shows the results of a simulation to determine the gender breakdown in 20 families.

Number of girls      0 1 2 3 4
Probability StartFraction 2 Over 20 EndFraction equals 0.1 StartFraction 4 Over 20 EndFraction equals 0.2 StartFraction 6 Over 20 EndFraction equals 0.3 StartFraction 5 Over 20 EndFraction equals 0.25 StartFraction 3 Over 20 EndFraction equals 0.15



a. Based on the simulation results, which is more likely, a 2 colon 2 split of boys and girls or a 3 colon 1 split in either direction?

 split is more likely with a probability of .

b. Write out the sample space and calculate the exact probabilities for the various possible gender breakdowns.

Enter the exact answer as a decimal.

Number of girls      0 1 2 3 4
Probability



c. Reanswer part a. using exact probabilities.

 split is more likely with a probability of .

 

 

According to The World Almanac and Book of Facts 1999, approximately 25 % of all babies born in Texas are Hispanic. Consider a city in Texas with two hospitals, and suppose that Hospital A has 10 births per day, while Hospital B has 50 births per day.

Technology is used to simulate the births for 365 days at each of these two hospitals. Their histograms are displayed below.



a. Which hospital has more days on which more than 40 % of the babies born are Hispanic?



b. Which hospital has more days on which between 15 % and 35 % of the babies born are Hispanic?



c. Which hospital has more days on which less than 40 % of the babies born are Hispanic?



d. Explain how you could have answered parts a-c without the benefit of the simulation, based on what you learned in this topic about randomness and sample size.

The hospital with the  sample size is expected to have data that is more concentrated around its mean. Thus,  should have a greater percentage of Hispanic births between 15 % and 35 % and a smaller percentage away from the mean - greater than 40 %.

 

Body Temperatures

The histogram below displays the body temperatures (in degrees Fahrenheit) of 130 healthy adults (Shoemaker, 1996, BodyTemps).

a. Use technology to produce a normal probability plot of these data. Does a normal model seem to be appropriate for these data? 

 

 

 

b. Produce separate histograms and normal probability plots for men and women to determine for which gender does a normal model seem to be more appropriate. 

 

Subject Mathematics
Due By (Pacific Time) 04/03/2015 12:00 am
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