Question

One application of an absolute value inequality is the concept of the unfair coin. If a coin is tossed 100 times, we would expect approximately 50 of the tosses to be heads; however this is rarely the case.

1. Toss a coin 100 times to test this hypothesis. Record the number of times the coin is heads and the number of times the coin is tails on the lines below. You may want to ask someone to tally the results of the tosses for you.

Number of times the coin is heads Number of times the coin is tails

A coin is considered an unfair coin if h, the number of outcomes that result in heads, satisfies the inequality,

|(h-50)/5| ≥ 1.645

2. What values of h will tell us we have an unfair coin, if the coin is tossed 100 times? Show your work in the space provided here:

a. Solve the absolute value inequality, round to the nearest whole number.

b. Graph the solution.

c. Write the solution in interval notation.

3. Write a sentence that explains the solution to this inequality.

4. Based on the solution interval from problem if2, have you been tossing a fair or an unfair coin? Explain your answer in at least one complete sentence.

Answer 1

By tossing a coin 100 times,

Nember of times the coint is heads: 57 .

Namber of times the coin is fail: 43 .

|(h-50)/5|

=|(57-50)/5|

=7/5

=1.4 < 1.645

So the crin is arfair one.