Respuesta :
Answer:
The probability that a call last between 4.2 and 4.9 minutes is 0.4599
Step-by-step explanation:
Let X be the length in minutes of a random phone call. X is a normal distribution with mean λ=4.2 and standard deviation σ=0.4. We want to know P(4.2 < X < 4.9). In order to make computations, we will use W, the standarization of X, given by the following formula
[tex] W = \frac{X-\mu}{\sigma} = \frac{X-4.2}{0.4} [/tex]
We will use [tex] \phi [/tex] , the cummulative distribution function of W. The values of [tex] \phi [/tex] are well known and the can be found in the attached file
[tex]P(4.2 < X < 4.9) = P(\frac{4.2-4.2}{0.4} < \frac{X-4.2}{0.4} < \frac{4.9-4.2}{0.4}) = P(0 < W < 1.75) = \\ \phi(1.75) - \phi(0) = 0.9599-0.5 = 0.4599[/tex]
We conclude that the probability that a call last between 4.2 and 4.9 minutes is 0.4599
