Select the quadrant or access where are each ordered pair is located on a coordinate plane
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Answer:
This probability that the sample proportion is between 0.35 and 0.45 is the p-value of subtracted by the p-value of
. These p-values are found looking at the z-table.
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 establishes 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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Estimate of the proportion:
This is p, and thus, we use .
Sample of 160
This means that:
What is the probability that the sample proportion is between 0.35 and 0.45?
This probability that the sample proportion is between 0.35 and 0.45 is the p-value of subtracted by the p-value of
. These p-values are found looking at the z-table.