SOLUTION: Height of students entering the university has a normal distribution with a mean of 65 inches and a standard deviation of 5 inches. a.) What is the probability that a randomly se

Question 883623: Height of students entering the university has a normal distribution with a mean of 65 inches and a standard deviation of 5 inches.
a.) What is the probability that a randomly selected student has height between 55 inches and 72.5 inches
b.) researcher wants to examine students that are in the top 5% of this population, what is the minimum height in order to be considered as a subject for the study
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Height of students entering the university has a normal distribution with a mean of 65 inches and a standard deviation of 5 inches.
a.) What is the probability that a randomly selected student has height between 55 inches and 72.5 inches
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z(55) = (55-65)/5 = -2
z(72.5) = (72.5-65)/5 = 7.5/5 = 1.5
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P(55<= x <=72.5) = z(-2<= z < 1.5) = normalcdf(-2,1.5) = 0.9104
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b.) researcher wants to examine students that are in the top 5% of this population, what is the minimum height in order to be considered as a subject for the study.
Find the z-value with a right tail of 5%:
InvNorm(0.95) = 1.645
Find the corresponding height value:
x = 1.645*5+65
x = 73.22 inches
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Cheers,
Stan H.
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