Questions: Below are 36 sorted ages of an acting award winner. Find the percentile corresponding to age 44 using the method presented in the textbook. 17, 18, 19, 20, 22, 26, 28, 28, 31, 32, 33, 35, 36, 37, 39, 39, 39, 41, 43, 44, 50, 51, 53, 54, 55, 57, 58, 58, 59, 64, 65, 66, 72, 72, 73, 80 percentile of value 44 = (Round to the nearest integer as needed.)

Solution Steps

To find the percentile of age 44, we first need to determine the position of 44 in the sorted list of ages. The percentile rank can be calculated using the formula: \((\text{Number of values below } 44 + 0.5 \times \text{Number of values equal to } 44) / \text{Total number of values} \times 100\). This will give us the percentile rank of age 44.

To find the percentile of age 44, we first determine the number of ages below 44 in the sorted list. There are 19 ages below 44.

Next, we count the number of ages equal to 44. There is 1 age equal to 44.

The percentile rank of age 44 is calculated using the formula: \[ \text{Percentile} = \left(\frac{\text{Number of values below } 44 + 0.5 \times \text{Number of values equal to } 44}{\text{Total number of values}}\right) \times 100 \] Substituting the values, we have: \[ \text{Percentile} = \left(\frac{19 + 0.5 \times 1}{36}\right) \times 100 = 54.1667 \]

Finally, we round the percentile to the nearest integer: \[ \text{Percentile rounded} = 54 \]

Final Answer