deadman76751
13.04.2021 •
Mathematics
According to the Labor Department, the average duration of unemployment for adults ages 20 to 24 was 34.6 weeks during a recent month. Assume that the standard deviation for this population is 10.2 weeks. A random sample of 36 adults in this age group was selected. What is the probability that the average duration of unemployment was between 30 and 37 weeks
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Ответ:
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
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 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.
Mean of 34.6, standard deviation of 10.2
This means that
Sample of 36
This means that
What is the probability that the average duration of unemployment was between 30 and 37 weeks?
This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 30.
X = 37
By the Central Limit Theorem
has a pvalue of 0.9207
X = 30
has a pvalue of 0.0034
0.9207 - 0.0034 = 0.9173
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
Ответ:
2II
So that means
II+II= IV
Hope it helps ps have a great day:)