For a normally distributed data, with mean, μ, and standard deviation, σ, the probability that a randomly selected data, X, is less than a given value, x, is given by
[tex]P(X\ \textless \ x)=P \left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]
and the probability that a randomly selected data, X, is greater than a given value, x, is given by
[tex]P(X \ \textgreater \ x)=P \left(z\ \textgreater \ \frac{x-\mu}{\sigma} \right)=1-P \left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]
Given that the length of a social media interaction is normally distributed with a mean of 3 minutes and a standard deviation of 0.4 minutes, the probability that an interaction lasts longer than 4 minutes is given by
[tex]P(X\ \textgreater \ 4)=P\left(X\ \textgreater \ \frac{4-3}{0.4} \right) \\ \\ =P(X\ \textgreater \ 2.5)=1-P(X\ \textless \ 2.5)[/tex]
We use the normal distribution table or calculator to evalute that P(X < 2.5) = 0.99379
Therefore, the probability that an interaction lasts longer than 4 minutes = 1 - 0.99379 = 0.00621
[the last option]
