Question

1. When opening a bank account with a credit card, you will be asked to create a 4-digit PIN

number for debit transactions. From how many possible PIN numbers can you choose?
Explain your reasoning. (5 points)
2. The useful life of a radial tire is normally distributed with a mean of 80,000 miles and a
standard deviation of 5000 miles. A small tire company produces 10,000 tires a month.
a What is the probability that if you buy a radial tire at random, it will last between
70,000 and 85,000 miles? (1 point)
b. About how many tires from a month's production will last between 75,000 and
85,000 miles? (2 points)

Answer 1

1) 10000. When asked to pick a set of four decimal digits, then the total number of combinations possible are 10⁴. More generically speaking, if asked to pick a random set of n digits expressed in base b, then the total number of combinations available is bⁿ.

2a) 95%. According to the "Empirical Rule" 95% of data in a normal distribution falls within two standard deviations of the average.

2b) 68%. Again, using the Empirical Rule, we know that 68% fall within one standard deviation of the average.