STATISTICAL TECHNIQUES AND TOOLS
SAMPLING DISTRIBUTION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.Recently a sample of 25 tourists reported an average taxi fare of $23.20. What is the probability that a sample of 25 would have an average taxi fare greater than $23.20?
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.3752
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.6248
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.0559
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.9441
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Explanation:
Detailed explanation-1: -If mean of population is 25 then mean of sampling distribution is? If the mean of population is A=25, then the mean of sampling distribution of the mean is also A=25.
Detailed explanation-2: -For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean X= and standard deviation X=/√n, where n is the sample size.
Detailed explanation-3: -As the sample size increases the standard deviation of the distribution of sample means decreases. It is also true that the sampling distributions for successively larger samples approximate more and more closely a Gaussian distribution.
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