ACT Math 2 point
There are 280 runners registered for a race, and the
runners are divided into 4 age categories, as shown in
the table below
Age category:
under
16
16-25 26-35
over
35
Number of
runners:
40
76
112
52
The prize committee has 60 prizes to award and wants
the prizes to be awarded in proportion to the number of
runners registered in each category. How many prizes
should be designated for the 26-35 age category?
F. 15
G. 17
H. 24
J. 36
K. 40

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?