Question

1. a shopper went to a sale and bought a dvd player for $242. the mean price for this dvd player at all stores in the area was $280 with a standard deviation of $26. another shopper bought a tv for $486 that has a mean price of $548 with a standard deviation of $46. use the z - score to compare these two sales. which item is the better deal?
2. the ages that 25 randomly selected smokers started smoking were:

26 26 25 17 16 16 14 17 21 15 15 19 16
17 22 15 19 17 16 16 18 30 16 23 16
a) find the percentile rank for an age of 21.
b) find the percentile rank for an age of 17.

Explanation:

Step1: Sort the data

First, sort the data set in ascending order:
\(14,15,15,15,16,16,16,16,16,16,16,17,17,17,17,18,19,19,21,22,23,25,26,26,30\)

Step2: Calculate percentile rank for \(x = 21\)

The formula for percentile rank is \(PR=\frac{C+\frac{1}{2}F}{N}\times100\), where \(C\) is the number of values less than \(x\), \(F\) is the number of values equal to \(x\), and \(N\) is the total number of values.
For \(x = 21\), \(C = 18\), \(F = 1\), \(N=25\)
\(PR=\frac{18+\frac{1}{2}\times1}{25}\times100=\frac{18.5}{25}\times100 = 74\)

Step3: Calculate percentile rank for \(x = 17\)

For \(x = 17\), \(C = 11\), \(F = 4\), \(N = 25\)
\(PR=\frac{11+\frac{1}{2}\times4}{25}\times100=\frac{11 + 2}{25}\times100=\frac{13}{25}\times100=52\)

Answer:

a) \(74\)
b) \(52\)