1. a recent study reported that a typical american spends about 195 minutes (3 hours and 15 minutes) on…

1. a recent study reported that a typical american spends about 195 minutes (3 hours and 15 minutes) on their smartphone each day. the data shown gives the amount of time (in minutes) that each of 14 study participants spent on their smartphone on a given day. 74,114,128,161,188,192,216,222,230,258,280,356,378,402 which of the following is closest to the percentile of a participant who spent 230 minutes on their smartphone? a) 36 b) 43 c) 50 d) 57 e) 69

1. a recent study reported that a typical american spends about 195 minutes (3 hours and 15 minutes) on their smartphone each day. the data shown gives the amount of time (in minutes) that each of 14 study participants spent on their smartphone on a given day. 74,114,128,161,188,192,216,222,230,258,280,356,378,402 which of the following is closest to the percentile of a participant who spent 230 minutes on their smartphone? a) 36 b) 43 c) 50 d) 57 e) 69

Answer

Explanation:

Step1: Sort the data in ascending order

The data is already in ascending order: 74,114,128,161,188,192,216,222,230,258,280,356,378,402

Step2: Use the percentile formula

The formula for the $p^{th}$ percentile is $L=\frac{p}{100}(n + 1)$, where $n$ is the number of data - points. Here, $n = 14$. We want to find the percentile of the value 230. First, count the number of data - points less than or equal to 230. There are 8 data - points less than or equal to 230. The percentile $P=\frac{\text{Number of data - points less than or equal to the value}}{\text{Total number of data - points}}\times100=\frac{8}{14}\times100$

Step3: Calculate the percentile

$\frac{8}{14}\times100=\frac{800}{14}\approx57.14$

Answer:

D. 57