Sophie has 7 cookies she wants to share equally with ten friends at her party. Part A If she separates all of the cookies and gi
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Answer:
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
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 z-score 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 p-value, 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.
Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches.
This means that
Sample of 36:
This means that
Find the probability that they have a mean height greater than 72.3 inches.
This is 1 subtracted by the pvalue of Z when X = 72.3. So
By the Central Limit Theorem
has a pvalue of 0.9979
1 - 0.9979 = 0.0021
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
So,
Let the amount of the expensive coffee beans be x, and the amount of the less expensive coffee bean be y.
The number of pounds of coffee beans is 50.
x + y = 50
$8 times the amount of more expensive coffee beans plus $4 times the amount of less expensive coffee beans divided by 50 equals $6.50.
Now, all we have to do is use Elimination by Substitution.
x + y = 50
Subtract y from both sides.
x = 50 - y
Substitute 50 - y for x in the second equation.
Distribute.
Collect Like Terms.
Simplify.
Multiply both sides by 25.
Add 2y to both sides.
Subtract 162.5 from both sides.
37.5 = 2y
Divide both sides by 2.
18.75 = y
Substitute in an earlier equation to solve for x.
x = 50 - y
x = 50 - 18.75
x = 31.25
Check.
31.25 + 18.75 = 50 lbs.
6.50 = 6.50 This also checks.
There were 31.75 pounds of the more expensive coffee bean and 18.75 pounds of the less expensive coffee bean.
Let the amount of the expensive coffee beans be x, and the amount of the less expensive coffee bean be y.
The number of pounds of coffee beans is 50.
x + y = 50
$8 times the amount of more expensive coffee beans plus $4 times the amount of less expensive coffee beans divided by 50 equals $6.50.
Now, all we have to do is use Elimination by Substitution.
x + y = 50
Subtract y from both sides.
x = 50 - y
Substitute 50 - y for x in the second equation.
Distribute.
Collect Like Terms.
Simplify.
Multiply both sides by 25.
Add 2y to both sides.
Subtract 162.5 from both sides.
37.5 = 2y
Divide both sides by 2.
18.75 = y
Substitute in an earlier equation to solve for x.
x = 50 - y
x = 50 - 18.75
x = 31.25
Check.
31.25 + 18.75 = 50 lbs.
6.50 = 6.50 This also checks.
There were 31.75 pounds of the more expensive coffee bean and 18.75 pounds of the less expensive coffee bean.
Answer:
D. 151 cu. in.
Step-by-step explanation:
Given: Cone; Radius = 4 in, Height = 9 in.
To find: The volume of the specified cone
Formula:
Solution: A cone is a solid that has a circular base and a single vertex. To calculate its volume multiply the base area (area of a circle: π × r²) by height and by : volume = (
) × π × r² × h.