Respuesta :
Answer:
The probability that it will take less than 63 minnutes to complete the test is 0.1003
Step-by-step explanation:
Let X be the amount of time that takes to complete the test. X has Normal distribution with parameters [tex] \mu = 77 [/tex] and [tex] \sigma = 11 [/tex] . In order to find the probability of X being less than 63, we use the
standarization of X, which we will denote W. W is given by
[tex] W = \frac{X-\mu}{\sigma} = \frac{X-77}{11} [/tex]
The cumulative distribution function of W, which we denote [tex] \phi [/tex], has well known values. You can find the values of [tex] \phi [/tex] in the attached file.
Since the desnity function of a standard Normal distribution is symmetric, then we have that [tex] \phi(-x) = 1-\phi(x) [/tex] for any positive value x.
[tex]P(X< 63) = P(\frac{X-77}{11} < \frac{63-77}{11}) = P(W < -\frac{14}{11}) =\phi(-\frac{14}{11}) = 1-\phi(\frac{14}{11 }) = \\1 - \phi(1.28) = 1-0.8997 = 0.1003[/tex]
Therefore, the probability that it will take less than 63 minnutes to complete the test is 0.1003.
