Construct a sample (with at least two different values in the set) of 4 measurements whose mean, median, and mode are equal. If
1 answer:
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Answer:
<u>630</u> MP3 players are likely to be defective.
Step-by-step explanation:
Given:
A shipment to a warehouse consists of 4500 MP3 players the manager chooses a random sample of 50 MP3 players and finds that 7 are defective.
Now, to find the MP3 players which are likely to be defective.
Let the defective MP3 players be
Total MP3 players = 4500.
In sample of 50 MP3 players 7 are defective.
Now, setting the proportion:
If, 50 is equivalent to 7.
Then, 4500 is equivalent to
Now, to solve using cross multiplication method:
<em>By cross multiplying we get:</em>
<em /><em />
<em>Dividing both sides by 50 we get:</em>
Therefore, 630 MP3 players are likely to be defective.
Answer:
0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled
Step-by-step explanation:
To solve this question, we have 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?
This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So
X = 160
By the Central Limit Theorem
has a pvalue of 0.7257
X = 150
has a pvalue of 0.2743
0.7257 - 0.2743 = 0.4514
0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled