Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.
What is Probability ?
Probability is the measure of likelihood of an event.
For a Normal Distribution ,
the z-score formula is given by
[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]
Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .
It is the measure of the deviation of the data from its central tendency.
Each z-score has a probability value.
It is given in the question that
Mean of 2.16% = [tex]\rm \mu\\[/tex] = 2.16
Standard deviation of 1.36% means that [tex]\rm \sigma\\[/tex] = 1.36
For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]
s = 1.36/√31
s = 0.2442
Substituting the values
Z = (2.6 -2.16)/0.2442
Z =1.8
the p value from the graph of z and p , 0.9643
To determine value of probability more than X is 1 - 0.9643= 0.0357
the
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.
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