To estimate the probability of a sample proportion being greater than 0.50 in Region A and the sampling distribution of the difference in sample proportions between two regions, we use normal approximation and the Central Limit Theorem, involving statistical calculations based on known population proportions and sample sizes.
Explanation:To answer whether a polling agency's investigation into voter support for a ballot measure will have a sample proportion greater than 0.50 in Region A and to describe the sampling distribution of the difference in sample proportions (Region B minus Region A), including the probability that the two sample proportions differ by more than 0.05, we follow a statistical approach based on the Central Limit Theorem.
For Region A, assuming a population proportion of 0.47 and a sample size of 500, the probability of the sample proportion supporting the ballot measure being greater than 0.50 can be calculated using the normal approximation. This involves finding the z-score for the sample proportion and then using the standard normal distribution to find the associated probability.
For the sampling distribution of the difference in sample proportions (Region B minus Region A), we need to combine the variances of both sample proportions due to the Central Limit Theorem. This allows us to assess the probability that the two sample proportions will differ by more than 0.05 using a similar z-score and standard normal distribution approach.
The techniques applied involve the use of normal approximation to calculate probabilities and assumes a large enough sample size for the approximation to be accurate.
a 150 lb man has 2 beers, determine his BAC
BAC = ?
Answer: BAC = 0.056%
Explanation:-
Data given;
Weight of the man = 150 lbs (Wt)
Number of drinks = 2 beers
We know that
A beer contains 5% (0.05) of alcohol (D)
1 bear = 12oz
So 2 beer = 2 × 12 = 24oz (A)
Derived from widmark formula;
BAC for Male = (A × D × 5.14) / ( Wt × 0.73 )
BAC for Female = (A × D × 5.14) / ( Wt × 0.66 )
WHERE
A = Alcohol consumed in ounces (oz.)
D = percentage of alcohol written as a decimal
Wt = weight of person in pounds (lbs.)
Using BAC for male
BAC for Male = (A × D × 5.14) / ( Wt × 0.73 )
We simply input our values
BAC = ( 24 × 0.05 × 5.14) / ( 150 × 0.73)
BAC = 6.168 / 109.5
BAC = 0.056%
An ocean basin will form in what location, relative to the major tectonic plates?
Ocean basins can form at rift basins where continental crust is pulled apart and subsequently subsides, or at subduction zones where one plate dives beneath another. Ocean basins influence the size and movement of tectonic plates and can close over time, possibly leading to supercontinent formation.
Explanation:An ocean basin is likely to form at a location where continental crust is being pulled apart due to the process of rift basin formation. As the crust on both sides of the rift subsides, the area initially becomes a narrow sea and, if rifting continues, eventually develops into an ocean basin. The East African rift basin is an example of an early stage in this process. Additionally, other types of basins such as trench basins, forearc basins, and foreland basins are associated with different tectonic settings such as subduction zones and the mass of volcanic ranges.
Ocean basins are relatively young geological features, not exceeding 180 million years in age. The formation of ocean basins can significantly influence the size of oceanic and continental plates, such as the expansion of the Atlantic Ocean due to the mid-Atlantic ridge spreading, which is not counteracted by subduction except in certain regions like the Caribbean. In contrast, the Pacific Ocean is slowly getting smaller because its formation rate is outpaced by subduction processes, such as under North America at the Cascadia Subduction Zone.
Over geological time, as oceanic crust subducts beneath continental crust, ocean basins can close, leading to continental collision and the potential formation of a supercontinent. Known cycles of supercontinent formation and breakup have occurred throughout Earth's history approximately every 500 million years.