Convert 6.2x10^5 mm to km. (please show the steps to how you did the problem.)
2 answers:
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Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
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 normally distributed samples are 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.
For sums of size n, the mean is and the standard deviation is
In this question:
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
By the Central Limit Theorem
The 90th percentile for the distribution of the total contributions is $6,342,525.
Answer:
quarts
12 days
Step-by-step explanation:
Given that:
Amount of water leaked in 4 days = 3 quarts
To find:
Number of quarts leaked in 1 week?
Number of days taken for the leakage of 9 quarts of water?
Solution:
We can simply use unitary method or the ratio to find the answers of the questions asked in the statement.
As per question statement:
Amount of water leaked in 4 days = 3 quarts
Dividing by 4 on both sides:
Amount of water leaked in 1 day = quarts
Multiplying by 7 on both sides:
Amount of water leaked in 7 days = quarts
Number of days taken for the leakage of 3 quarts = 4 days
Multiplying by 3 on both sides:
Number of days taken for the leakage of 3 3 = 9 quarts = 4
3 = <em>12 days</em>