A number of people were asked how many days they would wait to seek medical treatment if they were suffering pain that interfered with their ability to work. The results are presented in the following table.
Number of days: 0 , 1 , 2 , 3 , 4 , 5
Frequency: 27 , 363 , 236 , 107, 19, 10
Consider this collection of people to be a population. Let X be the number of days for a person sampled at random for this population. Find the probability that a person would wait more than 2 days.
Write only a number as your answer. Round to four decimal places (for example: 0.5319). Do not write as a percentage.
X = (107+19+10)/(total frequency)
Consider these 827 people to be a population. Let X be the number of days for a person sampled at random from this population.
To find the probability that a person would wait more than 2 days, we need to calculate the cumulative frequency for all the values greater than 2, and then divide it by the total population size.
To calculate the cumulative frequency, we add up the frequencies for all the values 3, 4, and 5.
Cumulative Frequency = Frequency(3) + Frequency(4) + Frequency(5)
= 107 + 19 + 10
= 136
Next, we divide the cumulative frequency by the total population size to get the probability.
Probability = Cumulative Frequency / Total Population Size
= 136 / (27 + 363 + 236 + 107 + 19 + 10)
= 136 / 762
= 0.1785
Therefore, the probability that a person would wait more than 2 days is approximately 0.1785.