In: Statistics and Probability
Let X be the height of a student to be randomly selected at the University. Assume (for the purpose of modeling) that X has the normal distribution with a mean of 68 inches and a standard deviation of 4.9 inches.
a.) What is the probability a randomly selected student is shorter than 65 inches?
b.) What is the probability a randomly selected student is taller than 73 inches?
c.) What is the probability a randomly selected student's height falls within one standard deviation of the mean?
Here Let X be the height of a student to be randomly selected at the University.
Here mean height = = 68 inches
standard deviation = = 4.9 inches
(a) Pr(x < 65 inches) = NORMDIST(x < 65 inches ; 68 inches ; 4.9 inches)
Z = (65 - 68)/4.9 = -0.6122
Now we look into Z table or use excel NORMSDIST function
Pr(x < 65 inches) = Pr(Z < -0.6122)
= 0.2702
(b) Pr(x > 73 inches) = 1 - Pr(x < 73 inches) = 1 - NORMDIST(x < 73 inches ; 68 inches ; 4.9 inches)
Z = (73 - 68)/4.9 = 1.0204
Now we look into Z table or use excel NORMSDIST function
Pr(x > 73 inches) = 1 - Pr(Z > 1.0204) = 1 - 0.8462 = 0.1538
(c) As here we have to find the probability a randomly selected student's height falls within one standard deviation of the mean
Pr( - < x < + ) = Pr(x < + ) - Pr(x < - )
Z2 = 1
Z1 = -1
Pr( - < x < + ) = Pr(Z < 1) - Pr(Z < -1)
looking into z table we find probability value for Z = 1 and Z = -1
Pr( - < x < + ) = Pr(Z < 1) - Pr(Z < -1)
= 0.8413 - 0.1587 = 0.6827