Respuesta :
Answer:
a) 2.28% of the men are taller than 74 inches
b) 50% of the men are taller than 69 inches
c) 47.72% of the men are between 69 and 74 inches
Step-by-step explanation:
Let X represent the height of a randomly selected male. X has distribution N(μ = 69, σ = 2.5). Lets standarize X, calling W the standarization, which is given by the formula
[tex] W = \frac{X-\mu}{\sigma} = \frac{X-69}{2.5} \simeq N(0,1) [/tex]
Lets denote [tex] \phi [/tex] the cummulative distribution function of W. The values of [tex] \phi [/tex] can be founded in the attached file. With this standarization we can make computations.
a)
[tex] P(X > 74) = P(\frac{X-69}{2.5} > \frac{74-69}{2.5}) = P(W > 2) = 1-\phi(2) = 1-0.9772 = 0.0228 [/tex]
Therefore, only 2.28% of the men are taller than 74 inches.
b)
[tex] P(X > 69) = P(W > \frac{69-69}{2.5}) = P(W>0) = 1-\phi(0) = 1/2 [/tex]
Thus, 50% of the men are taller than 69 inches.
c)
[tex] P(69 < X < 74) = P(\frac{69-69}{2.5} < W < \frac{74-69}{2.5}) = P(0 < W < 2) = \phi(2) - \phi(0) = 0.9772-0.5 = 0.4772 [/tex]
As a consecuence, 47.72% of the men are between 69 and 74 inches.
