Question

The time it takes a student to walk from the dorm to the chemistry lab follows roughly a Normaldistribution with a mean of 20 minutes and a standard deviation of 3 minutes. Suppose you are waitingfor your friend at the chemistry lab. She is walking from the dorm to the lab. Fifteen minutes have alreadypassed since the time she left the dorm. What is the probability she will arrive at the chemistry lab withinthe next 10 minutes (for a total walking time of less than 25 minutes)?

Answer 1

95.15%

Explanation:

We have that the mean (m) is equal to 20, the standard deviation (sd) 3

They ask us for P (x <25)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / sd

We have all these values, replacing we have:

z = (25 - 20) / (3)

z = 1.66

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <1.66) = 0.9515

Which means that the probability that it arrives before 25 minutes is 95.15%