I WILL GIVE BRAINLIEST AND 50 POINTS!!!(ANSWER ALL QUESTIONS) Question 1(Multiple Choice Worth 4 points) Erica purchased adult a
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Answer:
Step-by-step explanation:
In order to solve this equation, let's see what we already know.
- We know two points on the graph <em>which we can use to find the slope</em>
That's about it.
However, this can come useful to find the slope between the two points, which is the slope for the entire graph (since this is linear). The slope between two points is usually defined as (change in y / change in x). Our two points are (18, 2017) and (48, 2212).
The change in y between our two points is , and the change in x is
. Our slope will then be
, which comes out to be approximately 6.5. Therefore, our slope is 6.5.
Now that we know the slope, we can substitute inside our equation in slope intercept form.
We have yet to find b, the y-intercept (how much the plane itself weighs). To find b, we can substitute a point on the graph into the equation and solve for b. We know that the point (18, 2017) is on the graph so let's use that.
Now that we know our y-intercept is 1900, we can create our equation by using the slope and the y-intercept.
Finally, to find the weight of the plane with 66 pounds of fuel, we can substitute 66 inside this equation as x.
So the plane weighed 2329 pounds with 66 gallons of fuel.
Hope this helped!
Answer:
a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces
b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 8.0 ounces and a standard deviation of 1.1 ounces.
This means that
(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?
means that
This probability is the pvalue of Z when X = 9.3. So
By the Central Limit Theorem
has a pvalue of 0.9959
0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces
(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?
means that
This probability is 1 subtracted by the pvalue of Z when X = 9. So
has a pvalue of 0.9871
1 - 0.9871 = 0.0129
0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces