**Answer:**

**a) **2.84% probability that he is late for his first lecture.

**b)** 5.112 days

**Step-by-step explanation:**

**When the distribution is normal, we use the z-score formula.**

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

**In this question, we have that:**

**a. Find the probability that he is late for his first lecture.**

This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So

has a pvalue of 0.9716

1 - 0.9716 = 0.0284

2.84% probability that he is late for his first lecture.

**b. Find the number of days per year he is likely to be late for his first lecture.**

Each day, 2.84% probability that he is late for his first lecture.

Out of 180

0.0284*180 = 5.112 days