3 a You are disappointed to hear you came in 250th place in

3. a) You are disappointed to hear you came in 250th place in a race. Your coach tells you to cheer up as 2000 people entered the race. What percentile corresponds to your place at the end of the race? b) A certain brand of tires have a mean life span of 35,000 miles and a standard deviation of 2250 miles. Assuming the life span of the tires have a bell-shaped distribution, use the ?Empirical Rule? to determine the percentile corresponding to a tire with a life span of 32,750 miles. c) How many license plate numbers are possible in a state where license plate numbers are two letters of the alphabet followed by four numerical digits (0 - 9) where repeat numbers and letters are allowed. d) A five-question multiple-choice test is given. If all five questions must be answered a, b, or c, in how many different ways can the five questions be answered?

Solution

250th place in a race of 2000 means (250/2000)

=12.5th percentile

-----------------------------------------------------------------------------------------------------

b) mu =35000 sigma =2250

For x score of 32750, z score = -1

Percentile with z score -1 is 15.87%

---------------------------------------------------------------------------------------

c) 2 letters and 4 digits

As repitition is allowed, no of ways = 26²(10)⁴

d) 5 questions and each has 3 choices.

All are independent and repitition is allowed for choices.

Hence no of ways = 3⁵