Question

(10) 2. ESP (extra sensory perception) is the ability to read minds. We have a set of cards with each card having one of 5 shapes on them (square, rectangle, triangle, circle, question mark) and there are an equal number of each shape in the deck. We are going to select one card from the deck, stare at it and then there is a guy who claims he has ESP who is going to guess at the shape on the card we drew out (after each time we pull a card out – the ESP dude will make a guess- then we put the card back ). We did this experiment 250 times and we count how many times he guesses correctly

a) Why does this an experiment that fits the criterion of a binomial?

b) What is the mean, standard deviation and normal range for the number of times he guesses correctly

c) If he guesses 55 correct do you think he has ESP? Explain

Answer 1

(a)

This is an experiment that fits the criterion of a binomial as follows:

(i) Totalnumber of trials = n = 250 is fixed

(ii) Probability of success in each trial = p =1/5 = 0.2 is the same for all trials

(iii) The trials are independent

(iv) Each trial has 2 mutually exclusive outcomes: success: guess at the shape on the card we drew out and failure :not guess at the shape on the card we drew out

(b)

(i) mean = = np = 250 X 0.2 = 50

(ii) standard deviation =

(iii) normal range for the number of times he guesses correctly is given by:

(c)

Binomial Distribution

n = 250

p = 0.2

q = 1 - p = 0.8

= 4.448 % < 5 %

Since the probability is less than 5%, we conclude that has ESP because probability of guessing 55 correct is less than 5% and it is a rare event.