Chapter 13.4, Problem 2CYU

To determine

To calculate:

The probability of new member that he will take class.

Answer to Problem 2CYU

The probability that a gym member signs up for the tae kwon do class is $0.40\%$ , yoga class is $35\%$ , swim class is $10\%$ , kick boxing class is $15\%$ .

Explanation of Solution

Given information:

Class	Frequency
Tae kwon do	$45\%$
Yoga	$30\%$
swimming	$15\%$
Kick-boxing	$10\%$

Calculation:

The following table describes the four classes at a gym and the percentage of gym members that sign up for each class.

Class	Frequency
Tae kwon do	$45\%$
Yoga	$30\%$
swimming	$15\%$
Kick-boxing	$10\%$

To simulate the gym classes and estimate the probability that a new gym member will signup for each class, that make a spinner with four segments that represent each percentage of gym members for each corresponding class.

Spin the spinner $20$ times and record the frequency of observed outcomes. The frequency of outcomes will vary between sets of $20$ spins. One such set of the spines can be recorded in a frequency table as the follows:

Outcome	Frequency
Tae kwon do	$8$
Yoga	$7$
swimming	$2$
Kick-boxing	$3$
Total	$20$

Now, divide each frequency in the frequency table to get the probabilities for each outcome.

Outcome	Frequency	Probability
Tae kwon do	$8$	$\frac{8}{20}=0.40$
Yoga	$7$	$\frac{7}{20}=0.35$
swimming	$2$	$\frac{2}{20}=0.10$
Kick-boxing	$3$	$\frac{3}{20}=0.15$
Total	$20$	$\frac{20}{20}=1$

Make a probability histogram by charting probability on the vertical axis and outcomes on the horizontal axis.

  

Hence, therefore the probability that a gym member signs up for the tae kwon do class is $0.40\%$ , yoga class is $35\%$ , swim class is $10\%$ , kick boxing class is $15\%$ .