In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively. What is the probability that a randomly selected smartphone user in the age range 13 to 55+ is at most 50.8 years old?

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

The values of the cummulative distribution function of W, which we will denote can be found in the attached file. Now we can calculate the probability we want

Thus, the probability that a randomly selected user's age is at most 50.8 is 0.8413.

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