SOMEONE PLEASE HELPP!!!!!!!!
2 answers:
A <em>proportional </em>relationship is one that maintains a constant ratio between the two values involved. For a quick example, say that 2 film tickets cost my $7. the ratio of tickets to dollars there would be 2/7. Naturally, if I wanted to buy twice as many tickets, it would cost me twice as much - I'd be paying $7 x 2 = $14 for 2 x 2 = 4 tickets, but the ratio - 2/7 - would be unchanged. That's a proportional relationship.
Here we're told that the relationship between a patient's body weight and the amount of medicine they receive is proportional, which means that the ratio between weight and medicine will stay the same, regardless of the weight of the patient. We're given one ratio: a 159 lb patient receives 212 mg of medicine, a ratio of 159/212. What we need to find is half of the other ratio; we're given that the patient weighs 129 lbs, but we aren't given the amount of medicine they receive. Let's call that amount m. What we <em>do </em>know is that these two quantities have a proportional relationship - the ratio between them never changes.
This means we can set the two ratios - 159/212 and 129/m - equal to each other:
The rest is fairly straightforward algebra:
So, we'll need 172 mg of medicine for a patient weighing 129 lbs.
(For that last calculation, I'd simply encourage you to use your calculator)
Alternatively:
If you want to avoid the hairy calculation at the end there, you can always try to reduce the ratio before moving on. In this case, with a little gruntwork, we can find that
Now we know that the ratio of medicine to body weight is (irreducably) 3 lbs to 4 mg of medicine.
A patient weighing 129 pounds weighs <em>43 times</em> that much, so naturally, we'd need to give them <em>43 times more medicine</em>, which works out to be 4 x 43 = 172 mg, as we'd expect.
Here we're told that the relationship between a patient's body weight and the amount of medicine they receive is proportional, which means that the ratio between weight and medicine will stay the same, regardless of the weight of the patient. We're given one ratio: a 159 lb patient receives 212 mg of medicine, a ratio of 159/212. What we need to find is half of the other ratio; we're given that the patient weighs 129 lbs, but we aren't given the amount of medicine they receive. Let's call that amount m. What we <em>do </em>know is that these two quantities have a proportional relationship - the ratio between them never changes.
This means we can set the two ratios - 159/212 and 129/m - equal to each other:
The rest is fairly straightforward algebra:
So, we'll need 172 mg of medicine for a patient weighing 129 lbs.
(For that last calculation, I'd simply encourage you to use your calculator)
Alternatively:
If you want to avoid the hairy calculation at the end there, you can always try to reduce the ratio before moving on. In this case, with a little gruntwork, we can find that
Now we know that the ratio of medicine to body weight is (irreducably) 3 lbs to 4 mg of medicine.
A patient weighing 129 pounds weighs <em>43 times</em> that much, so naturally, we'd need to give them <em>43 times more medicine</em>, which works out to be 4 x 43 = 172 mg, as we'd expect.
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Answer:
a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
Step-by-step explanation:
Question a:
We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a p-value of , so Z = 1.96.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.
The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.
The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
Question b:
The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
Answer:
1. P(X≥35) = 0.0183
2. P(X≤21) = 0.0183
3. P(0.18<p<0.25) = 0.7915
Step-by-step explanation:
We have the proportion for women: pw=0.22, and the proportion for men: pm=0.19.
1. We have a sample of 140 woman and we have to calculate the probability of getting 35 or more who do volunteer work.
This is equivalent to a proportion of
The standard error of the proportion is:
We calculate the z-score as:
Then, the probability of having 35 women or more who do volunteer work in this sample of 140 women is:
2. We have to calculate the probability of having 21 or fewer women in the group who do volunteer work.
The proportion is now:
We can calculate then the z-score as:
Then, the probability of having 21 women or less who do volunteer work in this sample of 140 women is:
3. For the sample with men and women, we use the proportion for both, which is π=0.2.
The sample size is n=300.
Then, the standard error of the proportion is:
We can calculate the z-scores for p1=0.18 and p2=0.25:
We can now calculate the probabilty of having a proportion within 0.18 and 0.25 as: