SOLUTION: The mean percent of childhood asthma prevalence in 43 cities is 2.21​%. A random sample of 34 of these cities is selected. What is the probability that the mean childhood asthma

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Question 1205902: The mean percent of childhood asthma prevalence in 43 cities is 2.21​%. A random sample of 34 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.4​%? Interpret this probability. Assume that the standard deviation is 1.22​%.
Answer by Theo(13342) About Me  (Show Source):
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the population mean percent is assumed to be 2.21.
this is based on a previous study of 43 cities.
the new sample size is 34 cities.
you want to know the probability that the mean of the new sample will be greater than 2.4%.
the population standard deviation is assumed to be 1.22%.

the sample error is equal to the standard deviation divided by the square root of the sample size = 1.22 / sqrt(34) = .2092282739.

z = (x-m)/s
z is the z-score
x is the new sample mean.
m is the assumed population mean.
s is the standard error.

z = (x-m)/s becomes z = (2.4-2.21)/.2092282739 = .9080990656.

the area under the normal distribution curve to the right of that z--score is equal to .1819129113.

that's the probability that the sample mean will be greater than 2.4%, assuming that the population mean is 2.21%, and that i have analyzed this correctly.