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ANSWER:
ANSWER:
According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets retu
1 answer:
Answer: 0.1
Step-by-step explanation:
Given : A Houston department store sampled 80 items sold in January and found that 8 of the items were returned.
In other words, sample size : <em>n</em>=1040
Number of items returned : <em>x</em>= 8
Let <em>p</em> be the proportion of items returned for the population of sales transactions at the Houston store.
As per sample , the sample proportion of items returned for the population of sales transactions at the Houston store is :
As we know that , <em>the sample proportion is the best estimate of the population proportion.</em>
Therefore,a point estimate of the proportion of items returned for the population of sales transactions at the Houston store is 0.1.
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Answer:
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
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
Proportion of 0.6
This means that
Sample of 46
This means that
Mean and standard deviation:
Probability of obtaining a sample proportion less than 0.5.
p-value of Z when X = 0.5. So
By the Central Limit Theorem
has a p-value of 0.0838
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
The function models Exponential Decay due to the fact that as
x -> infinity, y-> 0
x -> infinity, y-> 0