Question 235547: Tthe mean amount purchased by each customer at a casino is 23.50 euros. The population is positively skewed and the standard deviation is not known. A MARKETING REseARCHER TOOK A sample of 50 customers. If the standard deviation of the sample is 5 euros, what is the likelihood that the sample mean is greater than 22.5 but less then 25 euros
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The mean amount purchased by each customer at a casino is 23.50 euros.
The population is positively skewed and the standard deviation is not known.
A MARKETING REseARCHER TOOK A sample of 50 customers.
If the standard deviation of the sample is 5 euros, what is the likelihood that the sample mean is greater than 22.5 but less then 25 euros
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Although the population is not normally distributed, the sample means
will tend toward normality as n gets larger.
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Mean of the sample means: 23.50
If 5 euros is the std of the population, 5/Sqrt(50) is std of sample means:
t(25) = (25-23.5)/[5/sqrt(50)] = 2.1213
t(22.5) = (22.5-23.5)/[5/sqrt(50)] = -1.4142
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P(22.5 < x < 25) = P(-1.4142 < t < 2.1213 with df=49) = 0.8987 ===================================================================
Cheers,
Stan H.
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