# The Probability of Volunteers Receiving a Certificate of Merit

## What is the probability that a randomly selected volunteer will receive a certificate of merit if they worked less than 90 hours?

Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90?

## Answer:

The probability that a volunteer selected at random will receive a certificate of merit given that they worked less than 90 hours is less than 20%.

To determine the probability of a volunteer receiving a certificate of merit if they worked less than 90 hours, we need to consider the normal distribution of hours worked by volunteers at the hospital. The mean number of hours worked is 80 with a standard deviation of 7.

To find out how many standard deviations 90 hours are from the mean, we can use the formula (X - mean) / standard deviation. By calculating this, we can see that 90 hours is 1 standard deviation above the mean.

According to the 68-95-99.7 rule, approximately 68% of the data falls within one standard deviation of the mean. This means that a volunteer working less than 90 hours is within the range of one standard deviation above the mean.

Given that the top 20% of volunteers in terms of hours worked receive a certificate of merit, it is reasonable to assume that the likelihood of a randomly selected volunteer who worked less than 90 hours receiving a certificate of merit is high.