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IRINA_888 [86]
3 years ago
13

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a

standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?
Mathematics
1 answer:
Rainbow [258]3 years ago
6 0

Answer:

0.1587

Step-by-step explanation:

Let X be the commuting time for the student. We know that X\sim N(30, (5)^2). Then, the normal probability density function for the random variable X is given by

f(x) = \frac{1}{\sqrt{2\pi(5)^{2}}}\exp[-\frac{(x-\mu)^{2}}{2(5)^{2}}]. We are seeking the probability P(X>35) because the student leaves home at 8:25 A.M., we want to know the probability that the student will arrive at the college campus later than 9 A.M. and between 8:25 A.M. and 9 A.M. there are 35 minutes of difference. So,

 

P(X>35) = \int\limits_{35}^{\infty}f(x)dx = 0.1587

To find this probability you can use either a table from a book or a programming language. We have used the R statistical programming language an the instruction pnorm(35, mean = 30, sd = 5, lower.tail = F)

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