Respuesta :
Answer:
The probability that a randomly selected user's age is at most 50.8 is 0.8413
Step-by-step explanation:
Let X be the random variable that represents the ages of smartphone users. X has distribution N(μ = 36.9, σ = 13.9). In order to simplify computations, we will standarize X. we will consider W the random variable with distribution N(0,1) given by
[tex] W = \frac{X-\mu}{\sigma} = \frac{X-36.9}{13.9} [/tex]
The values of the cummulative distribution function of W, which we will denote [tex] \phi [/tex] can be found in the attached file. Now we can calculate the probability we want
[tex] P(X < 50.8) = P(\frac{X-36.9}{13.9} < \frac{50.8-36.9}{13.9}) = P(W < 1) = \phi(1) = 0.8413 [/tex]
Thus, the probability that a randomly selected user's age is at most 50.8 is 0.8413.
