15.12 State SAT scores. The correlation between the average SAT Mathematics score in the states and the percent of high school s
1 answer:
You might be interested in
Answer:
0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.
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.
Jean knows that the mean income level in the country is $40,000, with a standard deviation of $2,000.
This means that
Jean selected three neighborhoods and determined the average income level.
This means that
What is the probability that the average income level in the neighborhoods was less than $38,000
This is the pvalue of Z when X = 38000. So
By the Central Limit Theorem
has a pvalue of 0.0418
0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.
The mean of the weight is 8.1 ounces.
So the means of the distribution of 10 sample will be 10*8.1.
And the mean of 20 <span>cheese wedges is again 20*8.1.
(The mean of the addition of two normal law is the sum of the
mean of each law)
Divide the above two numbers: </span>
The distribution of the sample means of the weights of cheese wedges is multiplied by 2 in the new <span>batches</span>.
So the means of the distribution of 10 sample will be 10*8.1.
And the mean of 20 <span>cheese wedges is again 20*8.1.
(The mean of the addition of two normal law is the sum of the
mean of each law)
Divide the above two numbers: </span>
The distribution of the sample means of the weights of cheese wedges is multiplied by 2 in the new <span>batches</span>.